List questions from p-groups

Published on 12 Aug 2022 - 21:57

47

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An alternative notion of nilpotency class for $p$-groups

Published on 26 Mar 2026 - 12:34

82

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Finite subgroup containing all finite subgroups of infinite group

Published on 17 Sep 2022 - 18:31

409

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Let $G$ be a $p$-group and let $H$ be a proper subgroup of $G$. Show that $H$ is a proper subgroup of $N_G(H)$

Published on 24 Sep 2022 - 17:23

70

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Groups of order $p^3$, $p$ prime

Published on 03 Oct 2022 - 17:22

32

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Question on self-normalising $p$-subgroups of $p$-groups

Published on 10 Oct 2022 - 14:03

200

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Showing that $|X| \equiv |\text{Fix}(G)|\pmod{p}$.

Published on 17 Oct 2022 - 13:27

142

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Any group of order $p^2$ is abelian, where $p$ is prime; $G/Z(G)$ cyclic implies $G$ is cyclic.

Published on 17 Oct 2022 - 15:41

438

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Group of order $2p$ where $p$ is an odd prime is isomorphic to either integers mod $2p$ or dihedral group of order $2p$.

Published on 21 Oct 2022 - 14:29

157

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What are all the finite groups where every nontrivial element has order $3?$

Published on 27 Oct 2022 - 0:29

93

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How to show that $|G|=d_1^2+\cdots +d_s^2$ and $G$ is abelian?

Published on 28 Feb 2026 - 0:03

33

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Prove that $K’’=1$ for a particular $p$-group $K$

Published on 08 Nov 2022 - 14:35

49

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Image of augmentation ideal of a group ring under ring homomorphism.

Published on 26 Mar 2026 - 21:09

200

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Prove a simple module must be "trivial"

Published on 04 Jan 2023 - 13:36

118

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Show that this finite $p$-group is isomorphic to a product of two cyclic groups of the same order

Published on 10 Jan 2023 - 1:04

List Question

Are metacyclic $p$-groups semidirect products?

An alternative notion of nilpotency class for $p$-groups

Finite subgroup containing all finite subgroups of infinite group

Let $G$ be a $p$-group and let $H$ be a proper subgroup of $G$. Show that $H$ is a proper subgroup of $N_G(H)$

Groups of order $p^3$, $p$ prime

Question on self-normalising $p$-subgroups of $p$-groups

Showing that $|X| \equiv |\text{Fix}(G)|\pmod{p}$.

Any group of order $p^2$ is abelian, where $p$ is prime; $G/Z(G)$ cyclic implies $G$ is cyclic.

Group of order $2p$ where $p$ is an odd prime is isomorphic to either integers mod $2p$ or dihedral group of order $2p$.

What are all the finite groups where every nontrivial element has order $3?$

How to show that $|G|=d_1^2+\cdots +d_s^2$ and $G$ is abelian?

Prove that $K’’=1$ for a particular $p$-group $K$

Image of augmentation ideal of a group ring under ring homomorphism.

Prove a simple module must be "trivial"

Show that this finite $p$-group is isomorphic to a product of two cyclic groups of the same order

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