Question

Finding some explicit formula for $(ab)^n$ in any $a,b$ in a finite $p$-group.

score 233 · Answer 1 · 2018-12-18 09:27:15

233

Views

Finding some explicit formula for $(ab)^n$ in any $a,b$ in a finite $p$-group.

Published on 18 Dec 2018 - 9:27

score 353 · Answer 2 · 2026-03-23 12:13:38

353

Views

Intersection of all maximal subgroups of a finite group

Published on 23 Mar 2026 - 12:13

score 79 · Answer 3 · 2018-12-29 18:42:03

79

Views

If $P$ is a Sylow $p$-subgroup of $G$ then there exists a normal subgroup $K$ such that $G/K$ is isomorphic to $P/P \cap G'$

Published on 29 Dec 2018 - 18:42

score 426 · Answer 4 · 2018-12-30 12:19:07

426

Views

Finding the number of subgroups of $\mathbb{Z}_{p^3} \oplus \mathbb{Z}_{p^2} $.

Published on 30 Dec 2018 - 12:19

score 215 · Answer 5 · 2026-03-25 01:20:34

215

Views

Let $G$ be a non-abelian finite $p$-group, do we have $Z(G) \leq \Phi(G)$ in general?

Published on 25 Mar 2026 - 1:20

score 233 · Answer 6 · 2019-01-17 06:40:57

233

Views

Computing the class-preserving automorphism group of finite $p$-groups

Published on 17 Jan 2019 - 6:40

score 73 · Answer 7 · 2019-01-23 07:13:13

73

Views

If $\operatorname{class}(G) = 2$ and $\exp(G) = 4$ then $\exp(G') = 2$?

Published on 23 Jan 2019 - 7:13

score 147 · Answer 8 · 2019-01-29 08:53:38

147

Views

Order of elements of the Prüfer groups $\mathbb{Z}(p^{\infty})$

Published on 29 Jan 2019 - 8:53

score 92 · Answer 9 · 2019-02-04 15:54:53

92

Views

Maximal subgroup of Wreathed 2-groups

Published on 04 Feb 2019 - 15:54

score 133 · Answer 10 · 2019-02-04 16:53:04

133

Views

Let $G$ be group with order $p^n$; does there then exist a sequence of normal subgroups?

Published on 04 Feb 2019 - 16:53

score 377 · Answer 11 · 2019-02-05 09:35:22

377

Views

Cauchy's theorem proof clarification (group theory)

Published on 05 Feb 2019 - 9:35

score 61 · Answer 12 · 2019-02-17 17:35:58

61

Views

Does a list of elements' orders in an abelian group determine the group?

Published on 17 Feb 2019 - 17:35

score 56 · Answer 13 · 2019-02-18 04:33:48

56

Views

$p$-group problem

Published on 18 Feb 2019 - 4:33

score 103 · Answer 14 · 2019-02-20 22:45:42

103

Views

Rank of a $p$-group

Published on 20 Feb 2019 - 22:45

score 183 · Answer 15 · 2026-03-25 03:03:16

183

Views

Does non-abelian $\Phi(G)$ imply, that $p^5 | |G|$ for some prime $p$?

Published on 25 Mar 2026 - 3:03

List Question

Finding some explicit formula for $(ab)^n$ in any $a,b$ in a finite $p$-group.

Intersection of all maximal subgroups of a finite group

If $P$ is a Sylow $p$-subgroup of $G$ then there exists a normal subgroup $K$ such that $G/K$ is isomorphic to $P/P \cap G'$

Finding the number of subgroups of $\mathbb{Z}_{p^3} \oplus \mathbb{Z}_{p^2} $.

Let $G$ be a non-abelian finite $p$-group, do we have $Z(G) \leq \Phi(G)$ in general?

Computing the class-preserving automorphism group of finite $p$-groups

If $\operatorname{class}(G) = 2$ and $\exp(G) = 4$ then $\exp(G') = 2$?

Order of elements of the Prüfer groups $\mathbb{Z}(p^{\infty})$

Maximal subgroup of Wreathed 2-groups

Let $G$ be group with order $p^n$; does there then exist a sequence of normal subgroups?

Cauchy's theorem proof clarification (group theory)

Does a list of elements' orders in an abelian group determine the group?

$p$-group problem

Rank of a $p$-group

Does non-abelian $\Phi(G)$ imply, that $p^5 | |G|$ for some prime $p$?

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