Subgroups of $D_4$
$begingroup$
I need to determine the subgroups of the dihedral group of order 4, $D_4$.
I know that the elements of $D_4$ are ${1,r,r^2,r^3, s,rs,r^2s,r^3s}$
But I don't understand how to get the subgroups..
dihedral-groups
asked Oct 19 '13 at 16:18
user43418user43418
4582828
$endgroup$
|
show 1 more comment
$begingroup$
I need to determine the subgroups of the dihedral group of order 4, $D_4$.
I know that the elements of $D_4$ are ${1,r,r^2,r^3, s,rs,r^2s,r^3s}$
But I don't understand how to get the subgroups..
dihedral-groups
asked Oct 19 '13 at 16:18
user43418user43418
4582828
$endgroup$
$begingroup$
The elements don't do you any good unless you know generators/relations, or something else about D4 to get you the group structure. What do you know about D4 apart from the names of the elements?
$endgroup$
– Tyler
Oct 19 '13 at 16:19
$begingroup$
@Tyler we know that $D_4$ is generated by the rotation $r$ and the reflection $s$
$endgroup$
– user43418
Oct 19 '13 at 16:20
3
$begingroup$
It is very disrespectful to delete a question once you get an answer. You shouldn't do that again.
$endgroup$
– Pedro Tamaroff♦
Oct 19 '13 at 17:02
3
$begingroup$
@Pedro: in the OP's defense, the question was deleted only 39 seconds after the answer was posted. It is possible the the OP hadn't seen the answer appear yet.
$endgroup$
– Henning Makholm
Oct 19 '13 at 17:05
1
$begingroup$
@PedroTamaroff It is true I didn't see it..
$endgroup$
– user43418
Oct 19 '13 at 17:23
|
show 1 more comment
$begingroup$
I need to determine the subgroups of the dihedral group of order 4, $D_4$.
I know that the elements of $D_4$ are ${1,r,r^2,r^3, s,rs,r^2s,r^3s}$
But I don't understand how to get the subgroups..
dihedral-groups
asked Oct 19 '13 at 16:18
user43418user43418
4582828
$endgroup$
I need to determine the subgroups of the dihedral group of order 4, $D_4$.
I know that the elements of $D_4$ are ${1,r,r^2,r^3, s,rs,r^2s,r^3s}$
But I don't understand how to get the subgroups..
dihedral-groups
dihedral-groups
asked Oct 19 '13 at 16:18
user43418user43418
4582828
asked Oct 19 '13 at 16:18
user43418user43418
4582828
asked Oct 19 '13 at 16:18
user43418user43418
4582828
asked Oct 19 '13 at 16:18
user43418user43418
4582828
asked Oct 19 '13 at 16:18
user43418user43418
4582828
4582828
$begingroup$
The elements don't do you any good unless you know generators/relations, or something else about D4 to get you the group structure. What do you know about D4 apart from the names of the elements?
$endgroup$
– Tyler
Oct 19 '13 at 16:19
$begingroup$
@Tyler we know that $D_4$ is generated by the rotation $r$ and the reflection $s$
$endgroup$
– user43418
Oct 19 '13 at 16:20
3
$begingroup$
It is very disrespectful to delete a question once you get an answer. You shouldn't do that again.
$endgroup$
– Pedro Tamaroff♦
Oct 19 '13 at 17:02
3
$begingroup$
@Pedro: in the OP's defense, the question was deleted only 39 seconds after the answer was posted. It is possible the the OP hadn't seen the answer appear yet.
$endgroup$
– Henning Makholm
Oct 19 '13 at 17:05
1
$begingroup$
@PedroTamaroff It is true I didn't see it..
$endgroup$
– user43418
Oct 19 '13 at 17:23
|
show 1 more comment
$begingroup$
The elements don't do you any good unless you know generators/relations, or something else about D4 to get you the group structure. What do you know about D4 apart from the names of the elements?
$endgroup$
– Tyler
Oct 19 '13 at 16:19
$begingroup$
@Tyler we know that $D_4$ is generated by the rotation $r$ and the reflection $s$
$endgroup$
– user43418
Oct 19 '13 at 16:20
3
$begingroup$
It is very disrespectful to delete a question once you get an answer. You shouldn't do that again.
$endgroup$
– Pedro Tamaroff♦
Oct 19 '13 at 17:02
3
$begingroup$
@Pedro: in the OP's defense, the question was deleted only 39 seconds after the answer was posted. It is possible the the OP hadn't seen the answer appear yet.
$endgroup$
– Henning Makholm
Oct 19 '13 at 17:05
1
$begingroup$
@PedroTamaroff It is true I didn't see it..
$endgroup$
– user43418
Oct 19 '13 at 17:23
$begingroup$
The elements don't do you any good unless you know generators/relations, or something else about D4 to get you the group structure. What do you know about D4 apart from the names of the elements?
$endgroup$
– Tyler
Oct 19 '13 at 16:19
$begingroup$
The elements don't do you any good unless you know generators/relations, or something else about D4 to get you the group structure. What do you know about D4 apart from the names of the elements?
$endgroup$
– Tyler
Oct 19 '13 at 16:19
$begingroup$
@Tyler we know that $D_4$ is generated by the rotation $r$ and the reflection $s$
$endgroup$
– user43418
Oct 19 '13 at 16:20
$begingroup$
@Tyler we know that $D_4$ is generated by the rotation $r$ and the reflection $s$
$endgroup$
– user43418
Oct 19 '13 at 16:20
3
3
$begingroup$
It is very disrespectful to delete a question once you get an answer. You shouldn't do that again.
$endgroup$
– Pedro Tamaroff♦
Oct 19 '13 at 17:02
$begingroup$
It is very disrespectful to delete a question once you get an answer. You shouldn't do that again.
$endgroup$
– Pedro Tamaroff♦
Oct 19 '13 at 17:02
3
3
$begingroup$
@Pedro: in the OP's defense, the question was deleted only 39 seconds after the answer was posted. It is possible the the OP hadn't seen the answer appear yet.
$endgroup$
– Henning Makholm
Oct 19 '13 at 17:05
$begingroup$
@Pedro: in the OP's defense, the question was deleted only 39 seconds after the answer was posted. It is possible the the OP hadn't seen the answer appear yet.
$endgroup$
– Henning Makholm
Oct 19 '13 at 17:05
1
1
$begingroup$
@PedroTamaroff It is true I didn't see it..
$endgroup$
– user43418
Oct 19 '13 at 17:23
$begingroup$
@PedroTamaroff It is true I didn't see it..
$endgroup$
– user43418
Oct 19 '13 at 17:23
|
show 1 more comment
2 Answers
2
active
oldest
votes
$begingroup$
By Lagrange's Theorem, the possible orders are $1, 2, 4,$ and $8$.
The only subgroup of order $1$ is ${1}$ and the only subgroup of order $8$ is $D_4$.
If $D_4$ has an order $2$ subgroup, it must be isomorphic to $mathbb{Z}_2$ (this is the only group of order $2$ up to isomorphism). Such a group is cyclic, it is generated by an element of order $2$. Are there any such elements in $D_4$?
If $D_4$ has an order $4$ subgroup, it must be isomorphic to either $mathbb{Z}_4$ or $mathbb{Z}_2timesmathbb{Z}_2$ (these are the only groups of order $4$ up to isomorphism). In the former case, the group is cyclic, it is generated by an element of order $4$. Are there any such elements in $D_4$? In the latter case, the group is generated by two commuting elements of order $2$. Are there any such pairs of elements in $D_4$?
In summary, first find all the elements of order $2$ and all the elements of order $4$; each of them generates a cyclic subgroup. Then consider pairs of elements of order $2$ to find which of them generate subgroups isomorphic to $mathbb{Z}_2timesmathbb{Z}_2$.
answered Oct 19 '13 at 16:25
Michael AlbaneseMichael Albanese
63.2k1598303
$endgroup$
add a comment |
$begingroup$
The notes by K. Conrad have a nice answer: the dihedral group $D_n$ is generated by a rotation $r$ and a reflection $s$ subject to the relations $r^n=s^2=1$ and $(rs)^2=1$.
Proposition: Every subgroup of $D_n$ is cyclic or dihedral. A complete listing of the subgroups (including $1$ and $D_n$) is as follows:
$(1)$ $langle r^d rangle$ for all divisors $dmid n$.
$(2)$ $langle r^d,r^is rangle$, where $dmid n$ and $0le ile d-1 $.
Very nice pictures of the subgroup diagram of $D_4$ can be found here.
edited Apr 13 '17 at 12:21
Community♦
1
answered Sep 16 '16 at 15:31
Dietrich BurdeDietrich Burde
78.7k64387
$endgroup$
$begingroup$
Thank you very much, I was searching the subgroups of the dihedral group. I would love if your answer was to the question: What are the subgroups of ANY dihedral group? If it was like that, I would have found it in google easier!
$endgroup$
– Santropedro
Jan 16 '17 at 0:59
$begingroup$
Oh, you interpreted my comment not like I intended! Indeed your answer is for all the dihedral groups. I was trying to say that it would be better if the title of this question was for any dihedral group, making the question appear in my searches! I was avoiding questions that only worked for some specific dihedral group. Then I tried with this question and your answer helped me.
$endgroup$
– Santropedro
Jan 16 '17 at 14:17
$begingroup$
@Santropedro Oh, I apologize! It sounded liked you would love if my answer would have been for ANY dihedral group - reading it again it is different of course.
$endgroup$
– Dietrich Burde
Jan 16 '17 at 15:10
$begingroup$
Yes, communicating is hard sometimes! Note: Your answer helped me a lot, thanks!
$endgroup$
– Santropedro
Jan 16 '17 at 17:27
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
By Lagrange's Theorem, the possible orders are $1, 2, 4,$ and $8$.
The only subgroup of order $1$ is ${1}$ and the only subgroup of order $8$ is $D_4$.
If $D_4$ has an order $2$ subgroup, it must be isomorphic to $mathbb{Z}_2$ (this is the only group of order $2$ up to isomorphism). Such a group is cyclic, it is generated by an element of order $2$. Are there any such elements in $D_4$?
If $D_4$ has an order $4$ subgroup, it must be isomorphic to either $mathbb{Z}_4$ or $mathbb{Z}_2timesmathbb{Z}_2$ (these are the only groups of order $4$ up to isomorphism). In the former case, the group is cyclic, it is generated by an element of order $4$. Are there any such elements in $D_4$? In the latter case, the group is generated by two commuting elements of order $2$. Are there any such pairs of elements in $D_4$?
In summary, first find all the elements of order $2$ and all the elements of order $4$; each of them generates a cyclic subgroup. Then consider pairs of elements of order $2$ to find which of them generate subgroups isomorphic to $mathbb{Z}_2timesmathbb{Z}_2$.
answered Oct 19 '13 at 16:25
Michael AlbaneseMichael Albanese
63.2k1598303
$endgroup$
add a comment |
$begingroup$
By Lagrange's Theorem, the possible orders are $1, 2, 4,$ and $8$.
The only subgroup of order $1$ is ${1}$ and the only subgroup of order $8$ is $D_4$.
If $D_4$ has an order $2$ subgroup, it must be isomorphic to $mathbb{Z}_2$ (this is the only group of order $2$ up to isomorphism). Such a group is cyclic, it is generated by an element of order $2$. Are there any such elements in $D_4$?
If $D_4$ has an order $4$ subgroup, it must be isomorphic to either $mathbb{Z}_4$ or $mathbb{Z}_2timesmathbb{Z}_2$ (these are the only groups of order $4$ up to isomorphism). In the former case, the group is cyclic, it is generated by an element of order $4$. Are there any such elements in $D_4$? In the latter case, the group is generated by two commuting elements of order $2$. Are there any such pairs of elements in $D_4$?
In summary, first find all the elements of order $2$ and all the elements of order $4$; each of them generates a cyclic subgroup. Then consider pairs of elements of order $2$ to find which of them generate subgroups isomorphic to $mathbb{Z}_2timesmathbb{Z}_2$.
answered Oct 19 '13 at 16:25
Michael AlbaneseMichael Albanese
63.2k1598303
$endgroup$
add a comment |
$begingroup$
By Lagrange's Theorem, the possible orders are $1, 2, 4,$ and $8$.
The only subgroup of order $1$ is ${1}$ and the only subgroup of order $8$ is $D_4$.
If $D_4$ has an order $2$ subgroup, it must be isomorphic to $mathbb{Z}_2$ (this is the only group of order $2$ up to isomorphism). Such a group is cyclic, it is generated by an element of order $2$. Are there any such elements in $D_4$?
If $D_4$ has an order $4$ subgroup, it must be isomorphic to either $mathbb{Z}_4$ or $mathbb{Z}_2timesmathbb{Z}_2$ (these are the only groups of order $4$ up to isomorphism). In the former case, the group is cyclic, it is generated by an element of order $4$. Are there any such elements in $D_4$? In the latter case, the group is generated by two commuting elements of order $2$. Are there any such pairs of elements in $D_4$?
In summary, first find all the elements of order $2$ and all the elements of order $4$; each of them generates a cyclic subgroup. Then consider pairs of elements of order $2$ to find which of them generate subgroups isomorphic to $mathbb{Z}_2timesmathbb{Z}_2$.
answered Oct 19 '13 at 16:25
Michael AlbaneseMichael Albanese
63.2k1598303
$endgroup$
By Lagrange's Theorem, the possible orders are $1, 2, 4,$ and $8$.
The only subgroup of order $1$ is ${1}$ and the only subgroup of order $8$ is $D_4$.
If $D_4$ has an order $2$ subgroup, it must be isomorphic to $mathbb{Z}_2$ (this is the only group of order $2$ up to isomorphism). Such a group is cyclic, it is generated by an element of order $2$. Are there any such elements in $D_4$?
If $D_4$ has an order $4$ subgroup, it must be isomorphic to either $mathbb{Z}_4$ or $mathbb{Z}_2timesmathbb{Z}_2$ (these are the only groups of order $4$ up to isomorphism). In the former case, the group is cyclic, it is generated by an element of order $4$. Are there any such elements in $D_4$? In the latter case, the group is generated by two commuting elements of order $2$. Are there any such pairs of elements in $D_4$?
In summary, first find all the elements of order $2$ and all the elements of order $4$; each of them generates a cyclic subgroup. Then consider pairs of elements of order $2$ to find which of them generate subgroups isomorphic to $mathbb{Z}_2timesmathbb{Z}_2$.
answered Oct 19 '13 at 16:25
Michael AlbaneseMichael Albanese
63.2k1598303
edited Nov 27 '18 at 12:24
answered Oct 19 '13 at 16:25
Michael AlbaneseMichael Albanese
63.2k1598303
answered Oct 19 '13 at 16:25
Michael AlbaneseMichael Albanese
63.2k1598303
answered Oct 19 '13 at 16:25
Michael AlbaneseMichael Albanese
63.2k1598303
63.2k1598303
add a comment |
add a comment |
$begingroup$
The notes by K. Conrad have a nice answer: the dihedral group $D_n$ is generated by a rotation $r$ and a reflection $s$ subject to the relations $r^n=s^2=1$ and $(rs)^2=1$.
Proposition: Every subgroup of $D_n$ is cyclic or dihedral. A complete listing of the subgroups (including $1$ and $D_n$) is as follows:
$(1)$ $langle r^d rangle$ for all divisors $dmid n$.
$(2)$ $langle r^d,r^is rangle$, where $dmid n$ and $0le ile d-1 $.
Very nice pictures of the subgroup diagram of $D_4$ can be found here.
edited Apr 13 '17 at 12:21
Community♦
1
answered Sep 16 '16 at 15:31
Dietrich BurdeDietrich Burde
78.7k64387
$endgroup$
$begingroup$
Thank you very much, I was searching the subgroups of the dihedral group. I would love if your answer was to the question: What are the subgroups of ANY dihedral group? If it was like that, I would have found it in google easier!
$endgroup$
– Santropedro
Jan 16 '17 at 0:59
$begingroup$
Oh, you interpreted my comment not like I intended! Indeed your answer is for all the dihedral groups. I was trying to say that it would be better if the title of this question was for any dihedral group, making the question appear in my searches! I was avoiding questions that only worked for some specific dihedral group. Then I tried with this question and your answer helped me.
$endgroup$
– Santropedro
Jan 16 '17 at 14:17
$begingroup$
@Santropedro Oh, I apologize! It sounded liked you would love if my answer would have been for ANY dihedral group - reading it again it is different of course.
$endgroup$
– Dietrich Burde
Jan 16 '17 at 15:10
$begingroup$
Yes, communicating is hard sometimes! Note: Your answer helped me a lot, thanks!
$endgroup$
– Santropedro
Jan 16 '17 at 17:27
add a comment |
$begingroup$
The notes by K. Conrad have a nice answer: the dihedral group $D_n$ is generated by a rotation $r$ and a reflection $s$ subject to the relations $r^n=s^2=1$ and $(rs)^2=1$.
Proposition: Every subgroup of $D_n$ is cyclic or dihedral. A complete listing of the subgroups (including $1$ and $D_n$) is as follows:
$(1)$ $langle r^d rangle$ for all divisors $dmid n$.
$(2)$ $langle r^d,r^is rangle$, where $dmid n$ and $0le ile d-1 $.
Very nice pictures of the subgroup diagram of $D_4$ can be found here.
edited Apr 13 '17 at 12:21
Community♦
1
answered Sep 16 '16 at 15:31
Dietrich BurdeDietrich Burde
78.7k64387
$endgroup$
$begingroup$
Thank you very much, I was searching the subgroups of the dihedral group. I would love if your answer was to the question: What are the subgroups of ANY dihedral group? If it was like that, I would have found it in google easier!
$endgroup$
– Santropedro
Jan 16 '17 at 0:59
$begingroup$
Oh, you interpreted my comment not like I intended! Indeed your answer is for all the dihedral groups. I was trying to say that it would be better if the title of this question was for any dihedral group, making the question appear in my searches! I was avoiding questions that only worked for some specific dihedral group. Then I tried with this question and your answer helped me.
$endgroup$
– Santropedro
Jan 16 '17 at 14:17
$begingroup$
@Santropedro Oh, I apologize! It sounded liked you would love if my answer would have been for ANY dihedral group - reading it again it is different of course.
$endgroup$
– Dietrich Burde
Jan 16 '17 at 15:10
$begingroup$
Yes, communicating is hard sometimes! Note: Your answer helped me a lot, thanks!
$endgroup$
– Santropedro
Jan 16 '17 at 17:27
add a comment |
$begingroup$
The notes by K. Conrad have a nice answer: the dihedral group $D_n$ is generated by a rotation $r$ and a reflection $s$ subject to the relations $r^n=s^2=1$ and $(rs)^2=1$.
Proposition: Every subgroup of $D_n$ is cyclic or dihedral. A complete listing of the subgroups (including $1$ and $D_n$) is as follows:
$(1)$ $langle r^d rangle$ for all divisors $dmid n$.
$(2)$ $langle r^d,r^is rangle$, where $dmid n$ and $0le ile d-1 $.
Very nice pictures of the subgroup diagram of $D_4$ can be found here.
edited Apr 13 '17 at 12:21
Community♦
1
answered Sep 16 '16 at 15:31
Dietrich BurdeDietrich Burde
78.7k64387
$endgroup$
The notes by K. Conrad have a nice answer: the dihedral group $D_n$ is generated by a rotation $r$ and a reflection $s$ subject to the relations $r^n=s^2=1$ and $(rs)^2=1$.
Proposition: Every subgroup of $D_n$ is cyclic or dihedral. A complete listing of the subgroups (including $1$ and $D_n$) is as follows:
$(1)$ $langle r^d rangle$ for all divisors $dmid n$.
$(2)$ $langle r^d,r^is rangle$, where $dmid n$ and $0le ile d-1 $.
Very nice pictures of the subgroup diagram of $D_4$ can be found here.
edited Apr 13 '17 at 12:21
Community♦
1
answered Sep 16 '16 at 15:31
Dietrich BurdeDietrich Burde
78.7k64387
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
1
answered Sep 16 '16 at 15:31
Dietrich BurdeDietrich Burde
78.7k64387
answered Sep 16 '16 at 15:31
Dietrich BurdeDietrich Burde
78.7k64387
answered Sep 16 '16 at 15:31
Dietrich BurdeDietrich Burde
78.7k64387
78.7k64387
$begingroup$
Thank you very much, I was searching the subgroups of the dihedral group. I would love if your answer was to the question: What are the subgroups of ANY dihedral group? If it was like that, I would have found it in google easier!
$endgroup$
– Santropedro
Jan 16 '17 at 0:59
$begingroup$
Oh, you interpreted my comment not like I intended! Indeed your answer is for all the dihedral groups. I was trying to say that it would be better if the title of this question was for any dihedral group, making the question appear in my searches! I was avoiding questions that only worked for some specific dihedral group. Then I tried with this question and your answer helped me.
$endgroup$
– Santropedro
Jan 16 '17 at 14:17
$begingroup$
@Santropedro Oh, I apologize! It sounded liked you would love if my answer would have been for ANY dihedral group - reading it again it is different of course.
$endgroup$
– Dietrich Burde
Jan 16 '17 at 15:10
$begingroup$
Yes, communicating is hard sometimes! Note: Your answer helped me a lot, thanks!
$endgroup$
– Santropedro
Jan 16 '17 at 17:27
add a comment |
$begingroup$
Thank you very much, I was searching the subgroups of the dihedral group. I would love if your answer was to the question: What are the subgroups of ANY dihedral group? If it was like that, I would have found it in google easier!
$endgroup$
– Santropedro
Jan 16 '17 at 0:59
$begingroup$
Oh, you interpreted my comment not like I intended! Indeed your answer is for all the dihedral groups. I was trying to say that it would be better if the title of this question was for any dihedral group, making the question appear in my searches! I was avoiding questions that only worked for some specific dihedral group. Then I tried with this question and your answer helped me.
$endgroup$
– Santropedro
Jan 16 '17 at 14:17
$begingroup$
@Santropedro Oh, I apologize! It sounded liked you would love if my answer would have been for ANY dihedral group - reading it again it is different of course.
$endgroup$
– Dietrich Burde
Jan 16 '17 at 15:10
$begingroup$
Yes, communicating is hard sometimes! Note: Your answer helped me a lot, thanks!
$endgroup$
– Santropedro
Jan 16 '17 at 17:27
$begingroup$
Thank you very much, I was searching the subgroups of the dihedral group. I would love if your answer was to the question: What are the subgroups of ANY dihedral group? If it was like that, I would have found it in google easier!
$endgroup$
– Santropedro
Jan 16 '17 at 0:59
$begingroup$
Thank you very much, I was searching the subgroups of the dihedral group. I would love if your answer was to the question: What are the subgroups of ANY dihedral group? If it was like that, I would have found it in google easier!
$endgroup$
– Santropedro
Jan 16 '17 at 0:59
$begingroup$
Oh, you interpreted my comment not like I intended! Indeed your answer is for all the dihedral groups. I was trying to say that it would be better if the title of this question was for any dihedral group, making the question appear in my searches! I was avoiding questions that only worked for some specific dihedral group. Then I tried with this question and your answer helped me.
$endgroup$
– Santropedro
Jan 16 '17 at 14:17
$begingroup$
Oh, you interpreted my comment not like I intended! Indeed your answer is for all the dihedral groups. I was trying to say that it would be better if the title of this question was for any dihedral group, making the question appear in my searches! I was avoiding questions that only worked for some specific dihedral group. Then I tried with this question and your answer helped me.
$endgroup$
– Santropedro
Jan 16 '17 at 14:17
$begingroup$
@Santropedro Oh, I apologize! It sounded liked you would love if my answer would have been for ANY dihedral group - reading it again it is different of course.
$endgroup$
– Dietrich Burde
Jan 16 '17 at 15:10
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@Santropedro Oh, I apologize! It sounded liked you would love if my answer would have been for ANY dihedral group - reading it again it is different of course.
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– Dietrich Burde
Jan 16 '17 at 15:10
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Yes, communicating is hard sometimes! Note: Your answer helped me a lot, thanks!
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– Santropedro
Jan 16 '17 at 17:27
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Yes, communicating is hard sometimes! Note: Your answer helped me a lot, thanks!
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– Santropedro
Jan 16 '17 at 17:27
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$begingroup$
The elements don't do you any good unless you know generators/relations, or something else about D4 to get you the group structure. What do you know about D4 apart from the names of the elements?
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– Tyler
Oct 19 '13 at 16:19
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@Tyler we know that $D_4$ is generated by the rotation $r$ and the reflection $s$
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– user43418
Oct 19 '13 at 16:20
3
$begingroup$
It is very disrespectful to delete a question once you get an answer. You shouldn't do that again.
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– Pedro Tamaroff♦
Oct 19 '13 at 17:02
3
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@Pedro: in the OP's defense, the question was deleted only 39 seconds after the answer was posted. It is possible the the OP hadn't seen the answer appear yet.
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– Henning Makholm
Oct 19 '13 at 17:05
1
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@PedroTamaroff It is true I didn't see it..
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– user43418
Oct 19 '13 at 17:23