Computing quotients of group by elements of its lower exponent$-p$ central series
$begingroup$
Let $G$ be a finite $p−$group of number of generators $d$ and exponent$−p$ class $c$, that is $c$ is the smallest integer satisfying $P_c(G)=1$ in the series
$$
G=P_0(G)≥...≥P_{i−1}(G)≥P_i(G)≥...
$$
Where $P_i(G)=[P_{i−1}(G),G]P_{i−1}(G)^p$.
1/ Can you show me how to calculate $G/P_i(G)$´s using GAP system?
2/ Can you show me how to compute $G/P_1(G)$ using abelianisation and row-echelonisation (by hand)?
Thanks in advance
group-theory finite-groups gap computational-algebra
edited Dec 6 '18 at 11:47
ahulpke
7,1021026
asked Dec 6 '18 at 9:05
A.MessabA.Messab
527
$endgroup$
add a comment |
$begingroup$
Let $G$ be a finite $p−$group of number of generators $d$ and exponent$−p$ class $c$, that is $c$ is the smallest integer satisfying $P_c(G)=1$ in the series
$$
G=P_0(G)≥...≥P_{i−1}(G)≥P_i(G)≥...
$$
Where $P_i(G)=[P_{i−1}(G),G]P_{i−1}(G)^p$.
1/ Can you show me how to calculate $G/P_i(G)$´s using GAP system?
2/ Can you show me how to compute $G/P_1(G)$ using abelianisation and row-echelonisation (by hand)?
Thanks in advance
group-theory finite-groups gap computational-algebra
edited Dec 6 '18 at 11:47
ahulpke
7,1021026
asked Dec 6 '18 at 9:05
A.MessabA.Messab
527
$endgroup$
add a comment |
$begingroup$
Let $G$ be a finite $p−$group of number of generators $d$ and exponent$−p$ class $c$, that is $c$ is the smallest integer satisfying $P_c(G)=1$ in the series
$$
G=P_0(G)≥...≥P_{i−1}(G)≥P_i(G)≥...
$$
Where $P_i(G)=[P_{i−1}(G),G]P_{i−1}(G)^p$.
1/ Can you show me how to calculate $G/P_i(G)$´s using GAP system?
2/ Can you show me how to compute $G/P_1(G)$ using abelianisation and row-echelonisation (by hand)?
Thanks in advance
group-theory finite-groups gap computational-algebra
edited Dec 6 '18 at 11:47
ahulpke
7,1021026
asked Dec 6 '18 at 9:05
A.MessabA.Messab
527
$endgroup$
Let $G$ be a finite $p−$group of number of generators $d$ and exponent$−p$ class $c$, that is $c$ is the smallest integer satisfying $P_c(G)=1$ in the series
$$
G=P_0(G)≥...≥P_{i−1}(G)≥P_i(G)≥...
$$
Where $P_i(G)=[P_{i−1}(G),G]P_{i−1}(G)^p$.
1/ Can you show me how to calculate $G/P_i(G)$´s using GAP system?
2/ Can you show me how to compute $G/P_1(G)$ using abelianisation and row-echelonisation (by hand)?
Thanks in advance
group-theory finite-groups gap computational-algebra
group-theory finite-groups gap computational-algebra
edited Dec 6 '18 at 11:47
ahulpke
7,1021026
asked Dec 6 '18 at 9:05
A.MessabA.Messab
527
edited Dec 6 '18 at 11:47
ahulpke
7,1021026
asked Dec 6 '18 at 9:05
A.MessabA.Messab
527
edited Dec 6 '18 at 11:47
ahulpke
7,1021026
edited Dec 6 '18 at 11:47
ahulpke
7,1021026
edited Dec 6 '18 at 11:47
ahulpke
7,1021026
7,1021026
asked Dec 6 '18 at 9:05
A.MessabA.Messab
527
asked Dec 6 '18 at 9:05
A.MessabA.Messab
527
asked Dec 6 '18 at 9:05
A.MessabA.Messab
527
527
add a comment |
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
The series is in general called the $p$-central series, so the GAP command is PCentralSeries.
As for calculating it by hand, you might want to look at section 9.4.2 of Holt/Eick/O'Brien: Handbook of Computational Group Theory.
answered Dec 6 '18 at 11:57
ahulpkeahulpke
7,1021026
$endgroup$
$begingroup$
Many thanks professor, I hope I can ask you for explanations if I find some ambiguity following the process you guided me to. In fact I start reading your "Notes on Computational Group Theory" it is also very helpful, thanks again
$endgroup$
– A.Messab
Dec 6 '18 at 12:05
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The series is in general called the $p$-central series, so the GAP command is PCentralSeries.
As for calculating it by hand, you might want to look at section 9.4.2 of Holt/Eick/O'Brien: Handbook of Computational Group Theory.
answered Dec 6 '18 at 11:57
ahulpkeahulpke
7,1021026
$endgroup$
$begingroup$
Many thanks professor, I hope I can ask you for explanations if I find some ambiguity following the process you guided me to. In fact I start reading your "Notes on Computational Group Theory" it is also very helpful, thanks again
$endgroup$
– A.Messab
Dec 6 '18 at 12:05
add a comment |
$begingroup$
The series is in general called the $p$-central series, so the GAP command is PCentralSeries.
As for calculating it by hand, you might want to look at section 9.4.2 of Holt/Eick/O'Brien: Handbook of Computational Group Theory.
answered Dec 6 '18 at 11:57
ahulpkeahulpke
7,1021026
$endgroup$
$begingroup$
Many thanks professor, I hope I can ask you for explanations if I find some ambiguity following the process you guided me to. In fact I start reading your "Notes on Computational Group Theory" it is also very helpful, thanks again
$endgroup$
– A.Messab
Dec 6 '18 at 12:05
add a comment |
$begingroup$
The series is in general called the $p$-central series, so the GAP command is PCentralSeries.
As for calculating it by hand, you might want to look at section 9.4.2 of Holt/Eick/O'Brien: Handbook of Computational Group Theory.
answered Dec 6 '18 at 11:57
ahulpkeahulpke
7,1021026
$endgroup$
The series is in general called the $p$-central series, so the GAP command is PCentralSeries.
As for calculating it by hand, you might want to look at section 9.4.2 of Holt/Eick/O'Brien: Handbook of Computational Group Theory.
answered Dec 6 '18 at 11:57
ahulpkeahulpke
7,1021026
answered Dec 6 '18 at 11:57
ahulpkeahulpke
7,1021026
answered Dec 6 '18 at 11:57
ahulpkeahulpke
7,1021026
answered Dec 6 '18 at 11:57
ahulpkeahulpke
7,1021026
7,1021026
$begingroup$
Many thanks professor, I hope I can ask you for explanations if I find some ambiguity following the process you guided me to. In fact I start reading your "Notes on Computational Group Theory" it is also very helpful, thanks again
$endgroup$
– A.Messab
Dec 6 '18 at 12:05
add a comment |
$begingroup$
Many thanks professor, I hope I can ask you for explanations if I find some ambiguity following the process you guided me to. In fact I start reading your "Notes on Computational Group Theory" it is also very helpful, thanks again
$endgroup$
– A.Messab
Dec 6 '18 at 12:05
$begingroup$
Many thanks professor, I hope I can ask you for explanations if I find some ambiguity following the process you guided me to. In fact I start reading your "Notes on Computational Group Theory" it is also very helpful, thanks again
$endgroup$
– A.Messab
Dec 6 '18 at 12:05
$begingroup$
Many thanks professor, I hope I can ask you for explanations if I find some ambiguity following the process you guided me to. In fact I start reading your "Notes on Computational Group Theory" it is also very helpful, thanks again
$endgroup$
– A.Messab
Dec 6 '18 at 12:05
add a comment |
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