List questions from simple-groups

Published on 25 Mar 2026 - 17:34

111

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Automorphisms of $ SL(n,q) $ coming from $ GL(n,q) $

Published on 13 May 2023 - 15:43

126

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Every proper subgroup of a simple group containing an order 45 element has an index of at least 14

Published on 16 May 2023 - 19:01

113

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To what extent can we determine the simplicity or non-simplicity of groups based on their prime decompositions?

Published on 31 May 2023 - 17:55

44

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a doubt on the simplicity of the alternating group $A_n$ in Dummit&Foote's Abstract Algebra

Published on 19 Jun 2023 - 17:58

245

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There are no simple groups of order $264$

Published on 22 Jun 2023 - 0:04

474

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There are no simple groups of order $336$

Published on 22 Jun 2023 - 3:19

150

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There are no simple groups of order $480$

Published on 22 Jun 2023 - 23:10

208

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Is every finite simple group a quotient of a braid group?

Published on 25 Mar 2026 - 10:57

146

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Let $G$ be a finite simple non abelian group and $\{1\}\neq H\le G$ be such that $\vert C_{G}(H)\vert=\vert G:H \vert$. Then $H=G$.

Published on 30 Jun 2023 - 17:41

39

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Simplicity of the $A_5$

Published on 06 Jul 2023 - 3:41

79

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Finite non abelian simple groups whose order is not divisible by 8

Published on 07 Jul 2023 - 20:11

78

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Show that $ SL(2,5) $ has no subgroup isomorphic to $ A_5 $

Published on 10 Jul 2023 - 21:23

86

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Is there an explicit maximal simple group?

Published on 25 Mar 2026 - 7:47

209

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Show $G$ is isomorphic to $\mathbb{Z}_2 \times \mathbb{Z}_2$

Published on 19 Jul 2023 - 1:02

List Question

Natural group extension constructed from Schur cover and its outer automorphism group

Automorphisms of $ SL(n,q) $ coming from $ GL(n,q) $

Every proper subgroup of a simple group containing an order 45 element has an index of at least 14

To what extent can we determine the simplicity or non-simplicity of groups based on their prime decompositions?

a doubt on the simplicity of the alternating group $A_n$ in Dummit&Foote's Abstract Algebra

There are no simple groups of order $264$

There are no simple groups of order $336$

There are no simple groups of order $480$

Is every finite simple group a quotient of a braid group?

Let $G$ be a finite simple non abelian group and $\{1\}\neq H\le G$ be such that $\vert C_{G}(H)\vert=\vert G:H \vert$. Then $H=G$.

Simplicity of the $A_5$

Finite non abelian simple groups whose order is not divisible by 8

Show that $ SL(2,5) $ has no subgroup isomorphic to $ A_5 $

Is there an explicit maximal simple group?

Show $G$ is isomorphic to $\mathbb{Z}_2 \times \mathbb{Z}_2$

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