Question

If $H$ and $K$ are nilpotent normal subgroups then $C(HK)$ is non trivial

score 107 · Answer 1 · 2026-03-27 06:08:53

107

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If $H$ and $K$ are nilpotent normal subgroups then $C(HK)$ is non trivial

Published on 27 Mar 2026 - 6:08

score 2.8k · Answer 2 · 2026-03-28 13:11:07

2.8k

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How to find normal subgroups from a character table?

Published on 28 Mar 2026 - 13:11

score 336 · Answer 3 · 2026-04-02 19:54:19

336

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Show that if $K$ is a normal subgroup of $H$ such that $H/K$ is abelian, then K contains all of the 3-cycles.

Published on 02 Apr 2026 - 19:54

score 143 · Answer 4 · 2026-03-26 22:15:08

143

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Minimal Normal Subgroups of an elementary abelian p-group

Published on 26 Mar 2026 - 22:15

score 138 · Answer 5 · 2016-05-22 19:26:20

138

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Sylow theorems and normality

Published on 22 May 2016 - 19:26

score 1.6k · Answer 6 · 2016-05-24 09:07:13

1.6k

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For an action of $G$ on a set, every point of some orbit has the same stabilizer if and only if this stabilizer is a normal subgroup.

Published on 24 May 2016 - 9:07

score 175 · Answer 7 · 2016-05-24 13:18:31

175

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A group of order pq with a single subgroup of order p

Published on 24 May 2016 - 13:18

score 1.2k · Answer 8 · 2016-05-28 19:03:08

1.2k

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If the correspodence $aHbH=abH$ defines a group operation on the set of left cosets of $H$ in $G$, then show that $H$ is normal in $G$.

Published on 28 May 2016 - 19:03

score 670 · Answer 9 · 2016-05-29 19:45:25

670

Views

$S_4/H \simeq S_3$ where $H$ is a normal subgroup

Published on 29 May 2016 - 19:45

score 189 · Answer 10 · 2016-05-30 04:57:48

189

Views

Determing whether a subgroup is normal

Published on 30 May 2016 - 4:57

score 337 · Answer 11 · 2016-05-30 17:34:55

337

Views

Showing that a quotient group $G/N$ is isomorphic to $\mathbb{Z}_3$

Published on 30 May 2016 - 17:34

score 798 · Answer 12 · 2016-05-30 18:43:01

798

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A surjective homomorphism and normal subgroups

Published on 30 May 2016 - 18:43

score 483 · Answer 13 · 2016-05-30 20:25:46

483

Views

Showing that a subnormal series for a finite group $G$ can be made into a composition series for $G$

Published on 30 May 2016 - 20:25

score 1.6k · Answer 14 · 2016-05-31 06:06:18

1.6k

Views

Normal subgroups of matrices

Published on 31 May 2016 - 6:06

score 68 · Answer 15 · 2026-04-01 17:28:45

68

Views

Given homomorphism $\rho: G \times H \to G$, trouble verifying Homomorphism Theorem

Published on 01 Apr 2026 - 17:28

List Question

If $H$ and $K$ are nilpotent normal subgroups then $C(HK)$ is non trivial

How to find normal subgroups from a character table?

Show that if $K$ is a normal subgroup of $H$ such that $H/K$ is abelian, then K contains all of the 3-cycles.

Minimal Normal Subgroups of an elementary abelian p-group

Sylow theorems and normality

For an action of $G$ on a set, every point of some orbit has the same stabilizer if and only if this stabilizer is a normal subgroup.

A group of order pq with a single subgroup of order p

If the correspodence $aHbH=abH$ defines a group operation on the set of left cosets of $H$ in $G$, then show that $H$ is normal in $G$.

$S_4/H \simeq S_3$ where $H$ is a normal subgroup

Determing whether a subgroup is normal

Showing that a quotient group $G/N$ is isomorphic to $\mathbb{Z}_3$

A surjective homomorphism and normal subgroups

Showing that a subnormal series for a finite group $G$ can be made into a composition series for $G$

Normal subgroups of matrices

Given homomorphism $\rho: G \times H \to G$, trouble verifying Homomorphism Theorem

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