List questions from p-groups

Published on 26 Apr 2022 - 5:15

36

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Step in proof showing $p$-groups are product of cyclic groups

Published on 27 Apr 2022 - 18:26

87

Views

Center and abelianization of a finite p-group

Published on 27 Apr 2022 - 20:55

180

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On local group rings

Published on 24 May 2022 - 1:59

57

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Given the background, how to show any map onto a cyclic group of order $p$ is of this specific form?

Published on 31 May 2022 - 12:28

103

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Show that $q\mid |N_G(H\cap K)|$ where $H,K\in\mbox{Syl}_p(G)$ with $|G| = p^nq$.

Published on 01 Jun 2022 - 4:23

77

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Prove if $G$ is a finite nonabelian $p$-group, then $p^2\mid |{\rm Aut}(G)|$.

Published on 10 Jun 2022 - 16:59

70

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How we illustrate the Prüfer-$3$ group elements on the unit circle?

Published on 18 Jun 2022 - 10:30

87

Views

Let $G$ be finite & nonsimple such that all normal subgroups of $G$ are $p$-groups for a given prime $p$. Is it true that $G$ is also a $p$-group?

Published on 12 Jul 2022 - 15:42

217

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Classification of nilpotent groups via $p$-groups

Published on 26 Mar 2026 - 10:57

119

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Prove that every group of order $p^m$ with $p$ a prime number can be generated by $m$ elements

Published on 25 Jul 2022 - 4:14

161

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Let $G$ be a group order order $p^3$. Show for any $g,h \in G$, we have $g^p h = hg^p$

Published on 25 Jul 2022 - 18:40

148

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Smallest normal subgroup such that the factor group is a $p$-group

Published on 02 Aug 2022 - 14:01

92

Views

A question on a 2-group with an elementary Abelian maximal subgroup

Published on 25 Mar 2026 - 17:24

61

Views

$U^s = (U^p)^s$ and there exists a normal series with factor group a p-group

Published on 04 Aug 2022 - 21:25

List Question

component B in the commuting algebra

Step in proof showing $p$-groups are product of cyclic groups

Center and abelianization of a finite p-group

On local group rings

Given the background, how to show any map onto a cyclic group of order $p$ is of this specific form?

Show that $q\mid |N_G(H\cap K)|$ where $H,K\in\mbox{Syl}_p(G)$ with $|G| = p^nq$.

Prove if $G$ is a finite nonabelian $p$-group, then $p^2\mid |{\rm Aut}(G)|$.

How we illustrate the Prüfer-$3$ group elements on the unit circle?

Let $G$ be finite & nonsimple such that all normal subgroups of $G$ are $p$-groups for a given prime $p$. Is it true that $G$ is also a $p$-group?

Classification of nilpotent groups via $p$-groups

Prove that every group of order $p^m$ with $p$ a prime number can be generated by $m$ elements

Let $G$ be a group order order $p^3$. Show for any $g,h \in G$, we have $g^p h = hg^p$

Smallest normal subgroup such that the factor group is a $p$-group

A question on a 2-group with an elementary Abelian maximal subgroup

$U^s = (U^p)^s$ and there exists a normal series with factor group a p-group

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