List questions from simple-groups

Published on 14 Apr 2026 - 4:00

284

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Find the number of group homomorphism between $A_5$ and $S_5$.

Published on 13 Apr 2026 - 17:25

456

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Group of order $108$ not simple using Sylow theorems on Sylow-$2$-subgroups

Published on 15 Apr 2026 - 9:38

200

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$PSL(2,13)$ has no subgroup of prime index.

Published on 26 Apr 2026 - 2:45

508

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Let $G$ be a finite simple group and let $H\subset G$ be a abelian subgroup of index $|G:H|=p$. Prove that $H = \{e\}$.

Published on 16 Apr 2026 - 6:29

55

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Proof that if $G$ permutes the factors of $T^k$ transitively, $G$ is maximal in $T^k \rtimes G$

Published on 16 Apr 2026 - 11:50

86

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Does there exist some sort of classification of finite marginally simple groups?

Published on 25 Apr 2026 - 5:22

455

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Does there exist a characteristically simple group, which is not a direct product of simple groups?

Published on 25 Apr 2026 - 22:28

52

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Using the number of Sylow 2-subgoups of $G$.

Published on 14 Apr 2026 - 18:25

131

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simplicity of the Janko group $J_1$

Published on 13 Apr 2026 - 13:52

207

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Structure of the outer automorphism group of $D_n(q)$

Published on 15 Apr 2026 - 5:21

82

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Automorphisms of $D_4(q)$ (Chevalley group)

Published on 16 Apr 2026 - 1:19

349

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No simple groups of given order.

Published on 13 Apr 2026 - 23:51

205

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Why is the number of Sylow 2 subgroups of simple group with order 60 not able to be 1 or 3?

Published on 18 Apr 2026 - 6:56

123

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A finite non-abelian group of order $n$ that for every divisor of $n$ has a subgroup is not simple

Published on 13 Apr 2026 - 18:59

List Question

Is there a simple abelian group $G$ with infinite order?

Find the number of group homomorphism between $A_5$ and $S_5$.

Group of order $108$ not simple using Sylow theorems on Sylow-$2$-subgroups

$PSL(2,13)$ has no subgroup of prime index.

Let $G$ be a finite simple group and let $H\subset G$ be a abelian subgroup of index $|G:H|=p$. Prove that $H = \{e\}$.

Proof that if $G$ permutes the factors of $T^k$ transitively, $G$ is maximal in $T^k \rtimes G$

Does there exist some sort of classification of finite marginally simple groups?

Does there exist a characteristically simple group, which is not a direct product of simple groups?

Using the number of Sylow 2-subgoups of $G$.

simplicity of the Janko group $J_1$

Structure of the outer automorphism group of $D_n(q)$

Automorphisms of $D_4(q)$ (Chevalley group)

No simple groups of given order.

Why is the number of Sylow 2 subgroups of simple group with order 60 not able to be 1 or 3?

A finite non-abelian group of order $n$ that for every divisor of $n$ has a subgroup is not simple

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