Detailed usage of abelianisation and row-echelonisation?
0
$begingroup$
Let
$G=⟨x,ymid[[x,y],x]=x^2,(xyx)^4,x^4,y^4,(yx)^3y=x⟩$
with $p=2$.
I hope to show me in details how to compute $G/P_1(G)$(A polycyclic presentation for $G/P_1(G)$), where $P_1(G)$ is the second element in the exponent-$p$ central series(In this case it is the Frattini subgroup of $G$) using abelianisation and row-echelonisation!
group-theory p-groups
edited Nov 27 '18 at 20:18
Arturo Magidin
262k34586909
asked Nov 27 '18 at 10:59
A.MessabA.Messab
527
$endgroup$
add a comment |
0
$begingroup$
Let
$G=⟨x,ymid[[x,y],x]=x^2,(xyx)^4,x^4,y^4,(yx)^3y=x⟩$
with $p=2$.
I hope to show me in details how to compute $G/P_1(G)$(A polycyclic presentation for $G/P_1(G)$), where $P_1(G)$ is the second element in the exponent-$p$ central series(In this case it is the Frattini subgroup of $G$) using abelianisation and row-echelonisation!
group-theory p-groups
edited Nov 27 '18 at 20:18
Arturo Magidin
262k34586909
asked Nov 27 '18 at 10:59
A.MessabA.Messab
527
$endgroup$
1
$begingroup$
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
$endgroup$
– Gerry Myerson
Nov 27 '18 at 11:30
$begingroup$
Sorry, it didn´t appear like posted!
$endgroup$
– A.Messab
Nov 27 '18 at 11:58
1
$begingroup$
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
$endgroup$
– YCor
Nov 27 '18 at 13:25
$begingroup$
You should also include the more general tag group-theory, since otherwise many people (including myself) will not see it. (I only saw it because of the link from the MathOverflow post.)
$endgroup$
– Derek Holt
Nov 27 '18 at 14:19
add a comment |
0
0
0
$begingroup$
Let
$G=⟨x,ymid[[x,y],x]=x^2,(xyx)^4,x^4,y^4,(yx)^3y=x⟩$
with $p=2$.
I hope to show me in details how to compute $G/P_1(G)$(A polycyclic presentation for $G/P_1(G)$), where $P_1(G)$ is the second element in the exponent-$p$ central series(In this case it is the Frattini subgroup of $G$) using abelianisation and row-echelonisation!
group-theory p-groups
edited Nov 27 '18 at 20:18
Arturo Magidin
262k34586909
asked Nov 27 '18 at 10:59
A.MessabA.Messab
527
$endgroup$
Let
$G=⟨x,ymid[[x,y],x]=x^2,(xyx)^4,x^4,y^4,(yx)^3y=x⟩$
with $p=2$.
I hope to show me in details how to compute $G/P_1(G)$(A polycyclic presentation for $G/P_1(G)$), where $P_1(G)$ is the second element in the exponent-$p$ central series(In this case it is the Frattini subgroup of $G$) using abelianisation and row-echelonisation!
group-theory p-groups
group-theory p-groups
edited Nov 27 '18 at 20:18
Arturo Magidin
262k34586909
asked Nov 27 '18 at 10:59
A.MessabA.Messab
527
edited Nov 27 '18 at 20:18
Arturo Magidin
262k34586909
asked Nov 27 '18 at 10:59
A.MessabA.Messab
527
edited Nov 27 '18 at 20:18
Arturo Magidin
262k34586909
edited Nov 27 '18 at 20:18
Arturo Magidin
262k34586909
edited Nov 27 '18 at 20:18
Arturo Magidin
262k34586909
262k34586909
asked Nov 27 '18 at 10:59
A.MessabA.Messab
527
asked Nov 27 '18 at 10:59
A.MessabA.Messab
527
asked Nov 27 '18 at 10:59
A.MessabA.Messab
527
527
1
$begingroup$
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
$endgroup$
– Gerry Myerson
Nov 27 '18 at 11:30
$begingroup$
Sorry, it didn´t appear like posted!
$endgroup$
– A.Messab
Nov 27 '18 at 11:58
1
$begingroup$
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
$endgroup$
– YCor
Nov 27 '18 at 13:25
$begingroup$
You should also include the more general tag group-theory, since otherwise many people (including myself) will not see it. (I only saw it because of the link from the MathOverflow post.)
$endgroup$
– Derek Holt
Nov 27 '18 at 14:19
add a comment |
1
$begingroup$
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
$endgroup$
– Gerry Myerson
Nov 27 '18 at 11:30
$begingroup$
Sorry, it didn´t appear like posted!
$endgroup$
– A.Messab
Nov 27 '18 at 11:58
1
$begingroup$
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
$endgroup$
– YCor
Nov 27 '18 at 13:25
$begingroup$
You should also include the more general tag group-theory, since otherwise many people (including myself) will not see it. (I only saw it because of the link from the MathOverflow post.)
$endgroup$
– Derek Holt
Nov 27 '18 at 14:19
1
1
$begingroup$
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
$endgroup$
– Gerry Myerson
Nov 27 '18 at 11:30
$begingroup$
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
$endgroup$
– Gerry Myerson
Nov 27 '18 at 11:30
$begingroup$
Sorry, it didn´t appear like posted!
$endgroup$
– A.Messab
Nov 27 '18 at 11:58
$begingroup$
Sorry, it didn´t appear like posted!
$endgroup$
– A.Messab
Nov 27 '18 at 11:58
1
1
$begingroup$
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
$endgroup$
– YCor
Nov 27 '18 at 13:25
$begingroup$
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
$endgroup$
– YCor
Nov 27 '18 at 13:25
$begingroup$
You should also include the more general tag group-theory, since otherwise many people (including myself) will not see it. (I only saw it because of the link from the MathOverflow post.)
$endgroup$
– Derek Holt
Nov 27 '18 at 14:19
$begingroup$
You should also include the more general tag group-theory, since otherwise many people (including myself) will not see it. (I only saw it because of the link from the MathOverflow post.)
$endgroup$
– Derek Holt
Nov 27 '18 at 14:19
add a comment |
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1
$begingroup$
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
$endgroup$
– Gerry Myerson
Nov 27 '18 at 11:30
$begingroup$
Sorry, it didn´t appear like posted!
$endgroup$
– A.Messab
Nov 27 '18 at 11:58
1
$begingroup$
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
$endgroup$
– YCor
Nov 27 '18 at 13:25
$begingroup$
You should also include the more general tag group-theory, since otherwise many people (including myself) will not see it. (I only saw it because of the link from the MathOverflow post.)
$endgroup$
– Derek Holt
Nov 27 '18 at 14:19