Question

Quotient groups of $p$-groups

score 661 · Answer 1 · 2013-11-01 02:44:55

661

Views

Quotient groups of $p$-groups

Published on 01 Nov 2013 - 2:44

score 18.4k · Answer 2 · 2013-11-03 00:57:33

18.4k

Views

A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$

Published on 03 Nov 2013 - 0:57

score 119 · Answer 3 · 2013-11-04 18:49:11

119

Views

Without using any Sylow theorem, if every element is a $p$-element then $G$ is a $p$-group

Published on 04 Nov 2013 - 18:49

score 540 · Answer 4 · 2013-11-05 00:17:17

540

Views

Non-abelian group of order $p^3$ without semidirect products

Published on 05 Nov 2013 - 0:17

score 11.5k · Answer 5 · 2013-11-14 17:11:45

11.5k

Views

If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$

Published on 14 Nov 2013 - 17:11

score 208 · Answer 6 · 2026-02-23 08:27:05

208

Views

Is there an analogue of outer Space to study outer automorphisms of free pro-$p$ groups?

Published on 23 Feb 2026 - 8:27

score 215 · Answer 7 · 2013-11-18 19:58:28

215

Views

An example where $Z(Z_G(A))$ is not a subset of right Engel elements in a finite $p$-group

Published on 18 Nov 2013 - 19:58

score 302 · Answer 8 · 2013-11-18 21:41:13

302

Views

Orders of Elements in Minimal Generating sets of Abelian p-Groups

Published on 18 Nov 2013 - 21:41

score 4k · Answer 9 · 2013-11-18 23:56:52

4k

Views

Any irreducible representation of a $p$-group over a field of characteristic $p$ is trivial.

Published on 18 Nov 2013 - 23:56

score 176 · Answer 10 · 2013-12-03 11:55:43

176

Views

$G$ a finite $p-$group, $H < G$ (i.e, $H$ a subgroup of $G$, but $H \neq G$), prove that $H \neq N_G(H)$

Published on 03 Dec 2013 - 11:55

score 541 · Answer 11 · 2026-03-27 01:22:39

541

Views

Groups of order $p^5$

Published on 27 Mar 2026 - 1:22

score 33 · Answer 12 · 2013-12-14 10:15:32

33

Views

characters in p-groups

Published on 14 Dec 2013 - 10:15

score 225 · Answer 13 · 2013-12-16 03:58:30

225

Views

The $i$-th center $Z_{i}(G)$

Published on 16 Dec 2013 - 3:58

score 236 · Answer 14 · 2014-01-03 12:50:42

236

Views

Nonabelian group of order $p^4$

Published on 03 Jan 2014 - 12:50

score 593 · Answer 15 · 2014-01-04 08:37:12

593

Views

Let $G$ be a finite $p$-group with has more than one maximal subgroup. Prove that $G$ has at least $p+1$ maximal subgroups.

Published on 04 Jan 2014 - 8:37

List Question

Quotient groups of $p$-groups

A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$

Without using any Sylow theorem, if every element is a $p$-element then $G$ is a $p$-group

Non-abelian group of order $p^3$ without semidirect products

If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$

Is there an analogue of outer Space to study outer automorphisms of free pro-$p$ groups?

An example where $Z(Z_G(A))$ is not a subset of right Engel elements in a finite $p$-group

Orders of Elements in Minimal Generating sets of Abelian p-Groups

Any irreducible representation of a $p$-group over a field of characteristic $p$ is trivial.

$G$ a finite $p-$group, $H < G$ (i.e, $H$ a subgroup of $G$, but $H \neq G$), prove that $H \neq N_G(H)$

Groups of order $p^5$

characters in p-groups

The $i$-th center $Z_{i}(G)$

Nonabelian group of order $p^4$

Let $G$ be a finite $p$-group with has more than one maximal subgroup. Prove that $G$ has at least $p+1$ maximal subgroups.

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