Question

Automorphism group of a non_abelian p_group

score 82 · Answer 1 · 2015-03-31 07:40:48

82

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Automorphism group of a non_abelian p_group

Published on 31 Mar 2015 - 7:40

score 6.1k · Answer 2 · 2015-04-04 16:34:16

6.1k

Views

In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.

Published on 04 Apr 2015 - 16:34

score 99 · Answer 3 · 2015-04-12 15:18:41

99

Views

If a certain group action fixes every element $x$ such that $x^4=1$, then the action is trivial

Published on 12 Apr 2015 - 15:18

score 540 · Answer 4 · 2026-02-23 06:17:38

540

Views

Frobenius kernel is regular normal elementary abelian p-subgroup?

Published on 23 Feb 2026 - 6:17

score 7.3k · Answer 5 · 2015-04-24 21:08:07

7.3k

Views

Difference between definitions of $p$-subgroup and Sylow $p$-subgroup

Published on 24 Apr 2015 - 21:08

score 844 · Answer 6 · 2015-04-28 19:14:02

844

Views

$p$-group acting on a finite set

Published on 28 Apr 2015 - 19:14

score 510 · Answer 7 · 2015-05-08 08:42:20

510

Views

On a classification of all the characteristic subgroups of a finite abelian $p$-group.

Published on 08 May 2015 - 8:42

score 158 · Answer 8 · 2015-06-02 05:25:59

158

Views

under following conditions $G$ has only one subgroup of order $p$.

Published on 02 Jun 2015 - 5:25

score 40 · Answer 9 · 2015-06-20 18:03:50

40

Views

If $A\lhd B\lhd C$ with $[C:A]=p^n$, is there $D\lhd A$ with $D\subset C$ and $D/A$ a finite $p$-group?

Published on 20 Jun 2015 - 18:03

score 254 · Answer 10 · 2015-06-29 15:58:27

254

Views

Abelianization of a $p$ group.

Published on 29 Jun 2015 - 15:58

score 470 · Answer 11 · 2015-07-09 14:10:45

470

Views

$G$ non abelian, order $p^3$ ($p$ prime). Suppose that the center is $p^2$, prove that $\exists\ x$ outside of the center, of order p

Published on 09 Jul 2015 - 14:10

score 93 · Answer 12 · 2026-03-25 10:55:28

93

Views

Center of a maximal subgroup

Published on 25 Mar 2026 - 10:55

score 86 · Answer 13 · 2015-08-13 17:24:06

86

Views

need a 3-group with 3 generators

Published on 13 Aug 2015 - 17:24

score 78 · Answer 14 · 2015-08-15 17:29:20

78

Views

Let $ M $ be a maximal subgroup of a solvable group $ G $, and assume that $ G=MC $, for some cyclic subgroup $ C $.

Published on 15 Aug 2015 - 17:29

score 325 · Answer 15 · 2015-08-18 19:52:39

325

Views

p-group of class 2 with cyclic commutator subgroup

Published on 18 Aug 2015 - 19:52

List Question

Automorphism group of a non_abelian p_group

In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.

If a certain group action fixes every element $x$ such that $x^4=1$, then the action is trivial

Frobenius kernel is regular normal elementary abelian p-subgroup?

Difference between definitions of $p$-subgroup and Sylow $p$-subgroup

$p$-group acting on a finite set

On a classification of all the characteristic subgroups of a finite abelian $p$-group.

under following conditions $G$ has only one subgroup of order $p$.

If $A\lhd B\lhd C$ with $[C:A]=p^n$, is there $D\lhd A$ with $D\subset C$ and $D/A$ a finite $p$-group?

Abelianization of a $p$ group.

$G$ non abelian, order $p^3$ ($p$ prime). Suppose that the center is $p^2$, prove that $\exists\ x$ outside of the center, of order p

Center of a maximal subgroup

need a 3-group with 3 generators

Let $ M $ be a maximal subgroup of a solvable group $ G $, and assume that $ G=MC $, for some cyclic subgroup $ C $.

p-group of class 2 with cyclic commutator subgroup

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