Question

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

score 236 · Answer 1 · 2026-04-17 14:48:31

236

Views

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

Published on 17 Apr 2026 - 14:48

score 364 · Answer 2 · 2026-05-06 13:37:26

364

Views

Intersection of all maximal subgroups of a finite group

Published on 06 May 2026 - 13:37

score 82 · Answer 3 · 2026-04-16 03:31:33

82

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 16 Apr 2026 - 3:31

score 429 · Answer 4 · 2026-04-12 14:31:12

429

Views

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

Published on 12 Apr 2026 - 14:31

score 218 · Answer 5 · 2026-04-22 17:16:53

218

Views

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

Published on 22 Apr 2026 - 17:16

score 236 · Answer 6 · 2026-04-11 11:26:44

236

Views

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

Published on 11 Apr 2026 - 11:26

score 75 · Answer 7 · 2026-04-16 11:51:08

75

Views

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

Published on 16 Apr 2026 - 11:51

score 150 · Answer 8 · 2026-04-13 08:53:13

150

Views

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

Published on 13 Apr 2026 - 8:53

score 95 · Answer 9 · 2026-04-11 04:46:46

95

Views

Maximal subgroup of Wreathed 2-groups

Published on 11 Apr 2026 - 4:46

score 136 · Answer 10 · 2026-04-16 03:56:54

136

Views

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

Published on 16 Apr 2026 - 3:56

score 380 · Answer 11 · 2026-04-12 17:54:47

380

Views

Cauchy's theorem proof clarification (group theory)

Published on 12 Apr 2026 - 17:54

score 64 · Answer 12 · 2026-04-12 09:49:50

64

Views

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

Published on 12 Apr 2026 - 9:49

score 61 · Answer 13 · 2026-04-10 01:02:52

61

Views

$p$-group problem

Published on 10 Apr 2026 - 1:02

score 108 · Answer 14 · 2026-04-16 02:59:11

108

Views

Rank of a $p$-group

Published on 16 Apr 2026 - 2:59

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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