Question

Normal subgroups of direct product of non-abelian simple groups (Exercise 18 from Chapter 4.5 of Dummit's book)

score 160 · Answer 1 · 2022-07-02 22:47:15

160

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Normal subgroups of direct product of non-abelian simple groups (Exercise 18 from Chapter 4.5 of Dummit's book)

Published on 02 Jul 2022 - 22:47

score 424 · Answer 2 · 2022-07-13 00:19:55

424

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Let $G$ be a group of order $120$ has a normal subgroup of order $2$ or index $2$.

Published on 13 Jul 2022 - 0:19

score 110 · Answer 3 · 2022-07-25 10:46:41

110

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Minimal normal subgroups are either Abelian or a product of non-Abelian simple normal subgroups

Published on 25 Jul 2022 - 10:46

score 55 · Answer 4 · 2022-08-02 18:37:36

55

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Simple group order $168$ and $2$-transitive permutation subgroup of $S_7$

Published on 02 Aug 2022 - 18:37

score 52 · Answer 5 · 2026-03-25 07:44:06

52

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Frattini subgroup of a simple non abelian group

Published on 25 Mar 2026 - 7:44

score 239 · Answer 6 · 2022-08-10 22:15:40

239

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Wilson's proof of Iwasawa's Lemma

Published on 10 Aug 2022 - 22:15

score 51 · Answer 7 · 2022-08-11 09:23:26

51

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How to show certain subgroups of $S_p$ are simple?

Published on 11 Aug 2022 - 9:23

score 67 · Answer 8 · 2022-08-12 10:58:32

67

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Let $G$ be a simple group which acts on $\Omega$. Let $\alpha \in \Omega$ such that $|O(\alpha)|=p$. Prove the order of $p$-sylow subgroup is $p$.

Published on 12 Aug 2022 - 10:58

score 82 · Answer 9 · 2022-08-23 08:31:47

82

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Let $G$ be a simple group, $H\leq G,[G:H]=n$ Prove $G \cong K,K\leq{\rm Sym}(n)$.

Published on 23 Aug 2022 - 8:31

score 130 · Answer 10 · 2022-09-07 21:50:17

130

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Finite simple groups of order $p+1$

Published on 07 Sep 2022 - 21:50

score 955 · Answer 11 · 2022-09-17 16:47:37

955

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What is the reason that A5 is simple and A4 is not?

Published on 17 Sep 2022 - 16:47

score 266 · Answer 12 · 2022-09-20 21:04:05

266

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Is a group of order $2^kp$ not simple, where $p$ is a prime and $k$ is an positive integer?

Published on 20 Sep 2022 - 21:04

score 236 · Answer 13 · 2022-09-23 12:40:10

236

Views

Compact simple group which is not a Lie group

Published on 23 Sep 2022 - 12:40

score 94 · Answer 14 · 2022-09-26 17:24:32

94

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Projection of Direct Product of Nonabelian Simple Groups

Published on 26 Sep 2022 - 17:24

score 53 · Answer 15 · 2022-10-02 13:02:41

53

Views

Minimal irrep of $ PSL(2,p) $

Published on 02 Oct 2022 - 13:02

List Question

Normal subgroups of direct product of non-abelian simple groups (Exercise 18 from Chapter 4.5 of Dummit's book)

Let $G$ be a group of order $120$ has a normal subgroup of order $2$ or index $2$.

Minimal normal subgroups are either Abelian or a product of non-Abelian simple normal subgroups

Simple group order $168$ and $2$-transitive permutation subgroup of $S_7$

Frattini subgroup of a simple non abelian group

Wilson's proof of Iwasawa's Lemma

How to show certain subgroups of $S_p$ are simple?

Let $G$ be a simple group which acts on $\Omega$. Let $\alpha \in \Omega$ such that $|O(\alpha)|=p$. Prove the order of $p$-sylow subgroup is $p$.

Let $G$ be a simple group, $H\leq G,[G:H]=n$ Prove $G \cong K,K\leq{\rm Sym}(n)$.

Finite simple groups of order $p+1$

What is the reason that A5 is simple and A4 is not?

Is a group of order $2^kp$ not simple, where $p$ is a prime and $k$ is an positive integer?

Compact simple group which is not a Lie group

Projection of Direct Product of Nonabelian Simple Groups

Minimal irrep of $ PSL(2,p) $

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