Detailed usage of abelianisation and row-echelonisation?
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
261k32585906
asked Nov 27 '18 at 10:59
A.MessabA.Messab
507
add a comment |
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
261k32585906
asked Nov 27 '18 at 10:59
A.MessabA.Messab
507
1
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
– Gerry Myerson
Nov 27 '18 at 11:30
Sorry, it didn´t appear like posted!
– A.Messab
Nov 27 '18 at 11:58
1
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
– YCor
Nov 27 '18 at 13:25
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.)
– Derek Holt
Nov 27 '18 at 14:19
add a comment |
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
261k32585906
asked Nov 27 '18 at 10:59
A.MessabA.Messab
507
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
261k32585906
asked Nov 27 '18 at 10:59
A.MessabA.Messab
507
edited Nov 27 '18 at 20:18
Arturo Magidin
261k32585906
asked Nov 27 '18 at 10:59
A.MessabA.Messab
507
edited Nov 27 '18 at 20:18
Arturo Magidin
261k32585906
edited Nov 27 '18 at 20:18
Arturo Magidin
261k32585906
edited Nov 27 '18 at 20:18
Arturo Magidin
261k32585906
261k32585906
asked Nov 27 '18 at 10:59
A.MessabA.Messab
507
asked Nov 27 '18 at 10:59
A.MessabA.Messab
507
asked Nov 27 '18 at 10:59
A.MessabA.Messab
507
507
1
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
– Gerry Myerson
Nov 27 '18 at 11:30
Sorry, it didn´t appear like posted!
– A.Messab
Nov 27 '18 at 11:58
1
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
– YCor
Nov 27 '18 at 13:25
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.)
– Derek Holt
Nov 27 '18 at 14:19
add a comment |
1
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
– Gerry Myerson
Nov 27 '18 at 11:30
Sorry, it didn´t appear like posted!
– A.Messab
Nov 27 '18 at 11:58
1
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
– YCor
Nov 27 '18 at 13:25
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.)
– Derek Holt
Nov 27 '18 at 14:19
1
1
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
– Gerry Myerson
Nov 27 '18 at 11:30
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
– Gerry Myerson
Nov 27 '18 at 11:30
Sorry, it didn´t appear like posted!
– A.Messab
Nov 27 '18 at 11:58
Sorry, it didn´t appear like posted!
– A.Messab
Nov 27 '18 at 11:58
1
1
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
– YCor
Nov 27 '18 at 13:25
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
– YCor
Nov 27 '18 at 13:25
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.)
– Derek Holt
Nov 27 '18 at 14:19
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.)
– Derek Holt
Nov 27 '18 at 14:19
add a comment |
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1
Simul-posted to MO, mathoverflow.net/questions/316317/…, with no notice to either site ––– an abuse of the system.
– Gerry Myerson
Nov 27 '18 at 11:30
Sorry, it didn´t appear like posted!
– A.Messab
Nov 27 '18 at 11:58
1
at this point it's easy for you to delete either the MathSE or MathOF question, up to your choice.
– YCor
Nov 27 '18 at 13:25
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.)
– Derek Holt
Nov 27 '18 at 14:19