Question

Prove that the order of a group $G$ must equal $36$ if $|G| = 4p^2$ for some odd prime and it has a non-normal Sylow $p$-subgroup

score 55 · Answer 1 · 2019-12-09 03:13:37

55

Views

Prove that the order of a group $G$ must equal $36$ if $|G| = 4p^2$ for some odd prime and it has a non-normal Sylow $p$-subgroup

Published on 09 Dec 2019 - 3:13

score 519 · Answer 2 · 2019-12-09 04:16:49

519

Views

$S_3$ is indecomposable but not simple

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score 88 · Answer 3 · 2026-04-09 06:57:40

88

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score 179 · Answer 4 · 2026-03-31 13:47:40

179

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score 58 · Answer 5 · 2026-03-25 19:11:44

58

Views

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score 36 · Answer 6 · 2019-12-10 04:11:48

36

Views

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score 49 · Answer 7 · 2026-03-24 23:44:45

49

Views

group isomorphisms not decomposable into relabelling or row-col exchange sequences

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score 50 · Answer 8 · 2019-12-10 15:45:55

50

Views

How to find the character table of a group with 12 elements generated by $x$ and $y$ with $x^3=y^2$

Published on 10 Dec 2019 - 15:45

score 69 · Answer 9 · 2019-12-11 04:09:06

69

Views

Control of fusion of p-elements in a subgroup containing a Sylow p-subgroup

Published on 11 Dec 2019 - 4:09

score 57 · Answer 10 · 2019-12-12 02:55:56

57

Views

Let $G$ be a finite group with $|G| = 70$, suppose $a \in G$ satisfies $a^{21} = e$. Prove that $a^7 = e$. Which of the following proofs is wrong?

Published on 12 Dec 2019 - 2:55

score 166 · Answer 11 · 2026-03-25 19:11:15

166

Views

On Hungerford lemma about normalizer of $p$-subgroup

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score 48 · Answer 12 · 2026-04-09 16:21:27

48

Views

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Published on 09 Apr 2026 - 16:21

score 107 · Answer 13 · 2026-03-25 17:22:20

107

Views

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Published on 25 Mar 2026 - 17:22

score 539 · Answer 14 · 2026-04-09 00:48:56

539

Views

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Published on 09 Apr 2026 - 0:48

score 96 · Answer 15 · 2026-03-28 14:55:01

96

Views

Reduction of the $S_3$ group representation

Published on 28 Mar 2026 - 14:55

List Question

Prove that the order of a group $G$ must equal $36$ if $|G| = 4p^2$ for some odd prime and it has a non-normal Sylow $p$-subgroup

$S_3$ is indecomposable but not simple

How many non-isomorphic finite groups with exactly $n$ conjugacy classes are there?

A simple formula in finite group representation

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

group theory of finite abelian groups

group isomorphisms not decomposable into relabelling or row-col exchange sequences

How to find the character table of a group with 12 elements generated by $x$ and $y$ with $x^3=y^2$

Control of fusion of p-elements in a subgroup containing a Sylow p-subgroup

Let $G$ be a finite group with $|G| = 70$, suppose $a \in G$ satisfies $a^{21} = e$. Prove that $a^7 = e$. Which of the following proofs is wrong?

On Hungerford lemma about normalizer of $p$-subgroup

Presentation of SL$(2,\mathbb{Z}_p)$

Effect of Generators and Relations on a Finite Group's Order

In modular representation theory, what is a block?

Reduction of the $S_3$ group representation

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