List questions from sylow-theory

Published on 15 Jan 2024 - 17:35

49

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Group of order 60 and sylow subgroup counting

Published on 20 Jan 2024 - 6:02

65

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Is there an infinite nilpotent group with one Sylow subgroup that is not normal?

Published on 25 Mar 2026 - 16:02

108

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No simple group of order $p^nq^m$, with barely invoking Sylow theorems

Published on 27 Mar 2026 - 0:59

123

Views

Sylow $p$-Subgroups of $GL_n(\mathbb F_q)$

Published on 30 Jan 2024 - 2:28

72

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Some questions about the proof of the third Sylow theorem

Published on 03 Mar 2024 - 15:01

83

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Normal Sylow Subgroups of Solvable Groups

Published on 09 Mar 2024 - 0:02

52

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Classifying Groups of Order 42 with an element of Order 6

Published on 16 Mar 2024 - 10:48

170

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Find a group of order 5784 that does not have a normal subgroup of index 12

Published on 23 Mar 2024 - 18:10

670

Views

Let $G$ be a group of order 315 with a normal 3-Sylow subgroup. Prove $G$ is abelian.

Published on 03 Jan 2015 - 15:29

2.1k

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A group of order $12$ either has a normal $ 3$-Sylow subgroup or is isomorphic to $A_4$

Published on 03 Jan 2015 - 16:45

1.3k

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$|G|=24$ prove that $G$ is not simple

Published on 05 Jan 2015 - 14:22

141

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$\lvert G\rvert=24$ not simple by a counting arguments

Published on 05 Jan 2015 - 15:18

577

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Proof-verification group order 48 not simple

Published on 06 Jan 2015 - 0:09

124

Views

Simple Groups of Finite Order

Published on 06 Jan 2015 - 15:11

List Question

Orbits of same size under conjugation action of Sylow $p$-subgroups by a normal subgroup $H$

Group of order 60 and sylow subgroup counting

Is there an infinite nilpotent group with one Sylow subgroup that is not normal?

No simple group of order $p^nq^m$, with barely invoking Sylow theorems

Sylow $p$-Subgroups of $GL_n(\mathbb F_q)$

Some questions about the proof of the third Sylow theorem

Normal Sylow Subgroups of Solvable Groups

Classifying Groups of Order 42 with an element of Order 6

Find a group of order 5784 that does not have a normal subgroup of index 12

Let $G$ be a group of order 315 with a normal 3-Sylow subgroup. Prove $G$ is abelian.

A group of order $12$ either has a normal $ 3$-Sylow subgroup or is isomorphic to $A_4$

$|G|=24$ prove that $G$ is not simple

$\lvert G\rvert=24$ not simple by a counting arguments

Proof-verification group order 48 not simple

Simple Groups of Finite Order

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