List questions from sylow-theory

Published on 08 Dec 2019 - 15:46

1.4k

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Proof that if $G$ is an abelian group and $p||G|$ then there is only one Sylow p-subgroup where all of its elements have powers of a p.

Published on 08 Dec 2019 - 19:12

195

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Let $H$ be a normal p-subgroup of a group $G$. Proof $H$ is contained in $S$ for all $S$ Sylow p-subgroup of G.

Published on 09 Dec 2019 - 20:27

58

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Non-abelian finite group as a direct product of $p$-groups

Published on 25 Mar 2026 - 19:11

78

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Let $p$ be an odd prime and G be a group of order $4p^3$

Published on 10 Dec 2019 - 22:12

381

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Normal subgroups of a group of order $102$

Published on 11 Dec 2019 - 22:56

219

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Intersection of Sylow-subgroups are characteristic subgroup?

Published on 23 Feb 2026 - 3:57

95

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Normal Subgroups of Solvable Groups with elementary abelian Sylow 2 subgroup

Published on 25 Mar 2026 - 22:10

271

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Question on classification for group of order 20

Published on 25 Mar 2026 - 20:11

1k

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How many groups of order $125$ up to isomorphism?

Published on 15 Dec 2019 - 18:50

129

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Do Sylow subgroups distinguish representations?

Published on 26 Mar 2026 - 2:52

54

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There are $8$ conjugates of $H$ in $G$, where $H$ is a Sylow $p$-subgroup with $p=7$

Published on 22 Dec 2019 - 12:04

239

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Simple proof of Sylow's theorems for Abelian groups?

Published on 23 Dec 2019 - 6:18

139

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A Lemma about Sylow Subgroups

Published on 24 Dec 2019 - 18:43

104

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Simplifying a proof of Sylow's first theorem

Published on 25 Dec 2019 - 4:28

List Question

Nonabelian group of order $75$ cannot have a cyclic subgroup of order $25$

Proof that if $G$ is an abelian group and $p||G|$ then there is only one Sylow p-subgroup where all of its elements have powers of a p.

Let $H$ be a normal p-subgroup of a group $G$. Proof $H$ is contained in $S$ for all $S$ Sylow p-subgroup of G.

Non-abelian finite group as a direct product of $p$-groups

Let $p$ be an odd prime and G be a group of order $4p^3$

Normal subgroups of a group of order $102$

Intersection of Sylow-subgroups are characteristic subgroup?

Normal Subgroups of Solvable Groups with elementary abelian Sylow 2 subgroup

Question on classification for group of order 20

How many groups of order $125$ up to isomorphism?

Do Sylow subgroups distinguish representations?

There are $8$ conjugates of $H$ in $G$, where $H$ is a Sylow $p$-subgroup with $p=7$

Simple proof of Sylow's theorems for Abelian groups?

A Lemma about Sylow Subgroups

Simplifying a proof of Sylow's first theorem

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