Let k be an integer such that k divides n. Show that H = is a normal subgroup of Dn (Dihedral group). Then,...
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Let k be an integer such that k divides n. Show that H = is a normal subgroup of Dn (Dihedral group). Then, show that Dn/H is isomorphic to Dk.
I am totally lost here. I know in Dihedral group, r^n=e=s^2, srs=r^-1. However, I don't know how to proceed this question.
abstract-algebra
asked Nov 19 at 4:50
RandomThinker
192
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up vote
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Let k be an integer such that k divides n. Show that H = is a normal subgroup of Dn (Dihedral group). Then, show that Dn/H is isomorphic to Dk.
I am totally lost here. I know in Dihedral group, r^n=e=s^2, srs=r^-1. However, I don't know how to proceed this question.
abstract-algebra
asked Nov 19 at 4:50
RandomThinker
192
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 at 5:23
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Let k be an integer such that k divides n. Show that H = is a normal subgroup of Dn (Dihedral group). Then, show that Dn/H is isomorphic to Dk.
I am totally lost here. I know in Dihedral group, r^n=e=s^2, srs=r^-1. However, I don't know how to proceed this question.
abstract-algebra
asked Nov 19 at 4:50
RandomThinker
192
Let k be an integer such that k divides n. Show that H = is a normal subgroup of Dn (Dihedral group). Then, show that Dn/H is isomorphic to Dk.
I am totally lost here. I know in Dihedral group, r^n=e=s^2, srs=r^-1. However, I don't know how to proceed this question.
abstract-algebra
abstract-algebra
asked Nov 19 at 4:50
RandomThinker
192
asked Nov 19 at 4:50
RandomThinker
192
asked Nov 19 at 4:50
RandomThinker
192
asked Nov 19 at 4:50
RandomThinker
192
asked Nov 19 at 4:50
RandomThinker
192
192
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 at 5:23
add a comment |
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 at 5:23
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 at 5:23
Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 at 5:23
add a comment |
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Totally lost? Then first thing to do is to remind yourself of the definition of normal subgroup, and of $D_n/H$ (and second thing to do is to learn how to format mathematics on this website – check the Help menu).
– Gerry Myerson
Nov 19 at 5:23