List questions from characteristic-subgroups

Published on 06 May 2019 - 8:05

475

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On group quotient by a characteristic subgroup

Published on 19 Jun 2019 - 8:38

94

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Is my proof correct?: Let $K$ be a normal subgroup of a finite group $G$ and assume $|K|$ and $|G/K|$ are coprime. Prove $K$ is characteristic in $G$.

Published on 30 Jun 2019 - 4:29

5.5k

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Commutator subgroup $G'$ is a characteristic subgroup of $G$

Published on 23 Feb 2026 - 0:29

542

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Characteristic subgroups of a direct product of groups

Published on 29 Dec 2014 - 18:52

907

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$G$ is characteristically simple $\iff$ there is simple $T$ such that $G \cong T\times T \times \cdots \times T$

Published on 02 Jan 2015 - 1:25

81

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Bounds for Khukhro-Makarenko theorems

Published on 18 Oct 2019 - 20:18

700

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Automorphism on subgroup lift to the whole group

Published on 31 Oct 2019 - 12:03

43

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On marginal subgroups and automorphisms

Published on 20 Nov 2019 - 19:38

80

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Is the preimage of a characteristic subgroup characteristic?

Published on 22 Nov 2019 - 21:18

218

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Intersection of Sylow-subgroups are characteristic subgroup?

Published on 13 Dec 2019 - 15:58

38

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Characteristic subgroups of the group of unipotent matrices

Published on 02 Jan 2020 - 16:47

125

Views

Turning my short sloppy proof that $G \blacktriangleright H \blacktriangleright K$ then $G \blacktriangleright K$ into a concise and neat proof?

Published on 05 Jan 2020 - 22:40

78

Views

Do there exist characteristic subgroups, that are not quasiverbal?

Published on 18 Jan 2020 - 8:33

1.8k

Views

Prove that every subgroup of an infinite cyclic group is characteristic

Published on 07 Aug 2016 - 12:12

List Question

For what $n$ is $A_n$ a marginal subgroup of $S_n$?

On group quotient by a characteristic subgroup

Is my proof correct?: Let $K$ be a normal subgroup of a finite group $G$ and assume $|K|$ and $|G/K|$ are coprime. Prove $K$ is characteristic in $G$.

Commutator subgroup $G'$ is a characteristic subgroup of $G$

Characteristic subgroups of a direct product of groups

$G$ is characteristically simple $\iff$ there is simple $T$ such that $G \cong T\times T \times \cdots \times T$

Bounds for Khukhro-Makarenko theorems

Automorphism on subgroup lift to the whole group

On marginal subgroups and automorphisms

Is the preimage of a characteristic subgroup characteristic?

Intersection of Sylow-subgroups are characteristic subgroup?

Characteristic subgroups of the group of unipotent matrices

Turning my short sloppy proof that $G \blacktriangleright H \blacktriangleright K$ then $G \blacktriangleright K$ into a concise and neat proof?

Do there exist characteristic subgroups, that are not quasiverbal?

Prove that every subgroup of an infinite cyclic group is characteristic

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