Question

On the numbers of maximal subgroups of a $p$-group

score 1.4k · Answer 1 · 2014-05-23 16:49:14

1.4k

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On the numbers of maximal subgroups of a $p$-group

Published on 23 May 2014 - 16:49

score 90 · Answer 2 · 2014-05-23 18:59:37

90

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suppose $G$ is group,if $Aut(G)$ is abelian then $G$ is nilpotent from nilpotency class of at most 2.

Published on 23 May 2014 - 18:59

score 174 · Answer 3 · 2014-05-23 19:29:33

174

Views

every principal factor of a finite soluble group is elementary abelian.

Published on 23 May 2014 - 19:29

score 75 · Answer 4 · 2014-05-23 21:32:43

75

Views

Is there a 20-order abelian subgroup of $S_5$?

Published on 23 May 2014 - 21:32

score 224 · Answer 5 · 2014-05-24 11:58:24

224

Views

a group with specific orders of elements

Published on 24 May 2014 - 11:58

score 772 · Answer 6 · 2026-04-01 13:20:28

772

Views

Angle between roots in a root system

Published on 01 Apr 2026 - 13:20

score 117 · Answer 7 · 2014-05-24 17:28:47

117

Views

Proof that $A_4$ is the unique group of order $12$ with no subgroup of order six

Published on 24 May 2014 - 17:28

score 58 · Answer 8 · 2014-05-25 07:00:26

58

Views

Is it true that $a$ and $b$ should be disjoint permutations?

Published on 25 May 2014 - 7:00

score 560 · Answer 9 · 2014-05-25 11:57:29

560

Views

$SL(2, \mathbb F_3)$ does not have a subgroup of order $12$

Published on 25 May 2014 - 11:57

score 563 · Answer 10 · 2026-03-25 02:59:03

563

Views

Finite groups with a certain Frattini subgroup

Published on 25 Mar 2026 - 2:59

score 2.3k · Answer 11 · 2014-05-25 14:25:45

2.3k

Views

How to prove that $MN/M \cap N \cong (MN/M) \times (MN/ N )$ where $M,N$ are normal subgroups of $G$?

Published on 25 May 2014 - 14:25

score 178 · Answer 12 · 2026-03-25 16:06:53

178

Views

On $p$-groups with a unique minimal subgroup

Published on 25 Mar 2026 - 16:06

score 483 · Answer 13 · 2026-03-25 14:21:00

483

Views

Finite $p$-group in which all its maximal subgroups are cyclic

Published on 25 Mar 2026 - 14:21

score 159 · Answer 14 · 2014-05-25 18:30:24

159

Views

Automorphism group of $C_{p^2}$

Published on 25 May 2014 - 18:30

score 648 · Answer 15 · 2014-05-25 18:54:53

648

Views

Why is there no group of order 16 with 12 elements of order 8?

Published on 25 May 2014 - 18:54

List Question

On the numbers of maximal subgroups of a $p$-group

suppose $G$ is group,if $Aut(G)$ is abelian then $G$ is nilpotent from nilpotency class of at most 2.

every principal factor of a finite soluble group is elementary abelian.

Is there a 20-order abelian subgroup of $S_5$?

a group with specific orders of elements

Angle between roots in a root system

Proof that $A_4$ is the unique group of order $12$ with no subgroup of order six

Is it true that $a$ and $b$ should be disjoint permutations?

$SL(2, \mathbb F_3)$ does not have a subgroup of order $12$

Finite groups with a certain Frattini subgroup

How to prove that $MN/M \cap N \cong (MN/M) \times (MN/ N )$ where $M,N$ are normal subgroups of $G$?

On $p$-groups with a unique minimal subgroup

Finite $p$-group in which all its maximal subgroups are cyclic

Automorphism group of $C_{p^2}$

Why is there no group of order 16 with 12 elements of order 8?

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