Question

How do we know all Sylow $p$-subgroups of a given order are distinct?

score 1.6k · Answer 1 · 2017-03-16 02:49:16

1.6k

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How do we know all Sylow $p$-subgroups of a given order are distinct?

Published on 16 Mar 2017 - 2:49

score 55 · Answer 2 · 2017-03-28 11:34:21

55

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Two non-isomorphic ways to present a finite p-group as a semidirect product

Published on 28 Mar 2017 - 11:34

score 326 · Answer 3 · 2026-03-25 04:44:15

326

Views

$|G|=p^n$, $Z(G)=\langle w\rangle$, $Z(G)\subseteq$ a maximal subgroup; then $\exists f\in \operatorname{Aut}(G)\ , k\ne1\pmod p$ s.t. $ f(w)=w^k$?

Published on 25 Mar 2026 - 4:44

score 94 · Answer 4 · 2023-01-30 20:50:07

94

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Which $p$- groups satisfy $G^p\gamma_2(G)=G^p\gamma_3(G)$?

Published on 30 Jan 2023 - 20:50

score 47 · Answer 5 · 2023-02-15 17:53:44

47

Views

Height of $px$ in a $p$-group.

Published on 15 Feb 2023 - 17:53

score 88 · Answer 6 · 2023-02-18 13:27:05

88

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Minimal presentation of non-abelian group of order $p^3$ and exponent $p^2$

Published on 18 Feb 2023 - 13:27

score 41 · Answer 7 · 2023-02-28 04:37:27

41

Views

Is there a natural number $k$ such that for every prime $p$ there is a non-Abelian group of order $p^k$?

Published on 28 Feb 2023 - 4:37

score 170 · Answer 8 · 2023-03-22 13:51:25

170

Views

Non-$p$-torsion difference of $p$-torsion elements in a $p$-group

Published on 22 Mar 2023 - 13:51

score 68 · Answer 9 · 2023-03-31 22:06:53

68

Views

Structure Description of p-groups of nilpotency class 2, where p is an odd prime.

Published on 31 Mar 2023 - 22:06

score 78 · Answer 10 · 2023-04-07 10:57:05

78

Views

A quotient group of a $p$-group is a $p$-group

Published on 07 Apr 2023 - 10:57

score 55 · Answer 11 · 2023-04-13 17:15:31

55

Views

Is it possible to prove $(G:H)\equiv (N:H) \pmod{p}$ without using Orbit Stabilizer Theorem or Sylow Theorem?

Published on 13 Apr 2023 - 17:15

score 53 · Answer 12 · 2023-04-14 22:07:51

53

Views

Is this a non-degenerate bilinear form on a quotient of a special p-group?

Published on 14 Apr 2023 - 22:07

score 59 · Answer 13 · 2023-04-16 20:11:28

59

Views

Showing that the direct sum is an infinite $p$-group which is not nilpotent.

Published on 16 Apr 2023 - 20:11

score 67 · Answer 14 · 2026-02-23 08:27:02

67

Views

Let $|G|=p^a$. Prove that if $|N|=p^{a-1}\Rightarrow N\lhd G$

Published on 23 Feb 2026 - 8:27

score 51 · Answer 15 · 2023-05-08 18:31:08

51

Views

The Second Cohomology group with Coefficient in cyclic group of order 3.

Published on 08 May 2023 - 18:31

List Question

How do we know all Sylow $p$-subgroups of a given order are distinct?

Two non-isomorphic ways to present a finite p-group as a semidirect product

$|G|=p^n$, $Z(G)=\langle w\rangle$, $Z(G)\subseteq$ a maximal subgroup; then $\exists f\in \operatorname{Aut}(G)\ , k\ne1\pmod p$ s.t. $ f(w)=w^k$?

Which $p$- groups satisfy $G^p\gamma_2(G)=G^p\gamma_3(G)$?

Height of $px$ in a $p$-group.

Minimal presentation of non-abelian group of order $p^3$ and exponent $p^2$

Is there a natural number $k$ such that for every prime $p$ there is a non-Abelian group of order $p^k$?

Non-$p$-torsion difference of $p$-torsion elements in a $p$-group

Structure Description of p-groups of nilpotency class 2, where p is an odd prime.

A quotient group of a $p$-group is a $p$-group

Is it possible to prove $(G:H)\equiv (N:H) \pmod{p}$ without using Orbit Stabilizer Theorem or Sylow Theorem?

Is this a non-degenerate bilinear form on a quotient of a special p-group?

Showing that the direct sum is an infinite $p$-group which is not nilpotent.

Let $|G|=p^a$. Prove that if $|N|=p^{a-1}\Rightarrow N\lhd G$

The Second Cohomology group with Coefficient in cyclic group of order 3.

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