Question

Does there exist some sort of classification of finite "characteristically simple" groups?

score 131 · Answer 1 · 2026-02-23 02:10:53

131

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Does there exist some sort of classification of finite "characteristically simple" groups?

Published on 23 Feb 2026 - 2:10

score 444 · Answer 2 · 2026-02-23 02:12:27

444

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Find all characteristic subgroups of the Dihedral group $D_{12}$.

Published on 23 Feb 2026 - 2:12

score 603 · Answer 3 · 2026-02-23 02:06:15

603

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Is there a common notation for characteristic subgroups?

Published on 23 Feb 2026 - 2:06

score 69 · Answer 4 · 2026-02-23 02:14:50

69

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If $G$ is a product of subnormal $S$ and a $p$-group, does the $p$-group need to be normal to know $\mathbf{O}^p(G) = \mathbf{O}^p(S)$?

Published on 23 Feb 2026 - 2:14

score 69 · Answer 5 · 2026-02-23 02:05:30

69

Views

Characteristic subgroups and factorization

Published on 23 Feb 2026 - 2:05

score 243 · Answer 6 · 2026-02-23 02:11:10

243

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

Published on 23 Feb 2026 - 2:11

score 699 · Answer 7 · 2026-02-23 02:06:16

699

Views

Why do Automorphisms map maximal subgroups to maximal subgroups?

Published on 23 Feb 2026 - 2:06

score 633 · Answer 8 · 2026-02-23 02:06:51

633

Views

Proving Characteristic Subgroups are Transitive

Published on 23 Feb 2026 - 2:06

score 93 · Answer 9 · 2026-02-23 02:15:30

93

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Behaviour of restrictions of automorphisms of groups on characteristic subgroup under epimorphisms

Published on 23 Feb 2026 - 2:15

score 79 · Answer 10 · 2026-02-23 02:13:50

79

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

Published on 23 Feb 2026 - 2:13

score 72 · Answer 11 · 2026-02-23 02:07:51

72

Views

Does there exist a verbally simple group, which is not characteristically simple?

Published on 23 Feb 2026 - 2:07

score 134 · Answer 12 · 2026-02-23 02:13:49

134

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Group $N \triangleleft G$, $(|N|,|G/N|) = 1$, then $N$ is a characteristic subgroup of $G$.

Published on 23 Feb 2026 - 2:13

score 441 · Answer 13 · 2026-02-23 02:11:10

441

Views

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

Published on 23 Feb 2026 - 2:11

score 61 · Answer 14 · 2026-02-23 02:16:05

61

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Does there exist an Artinian verbally simple group, which is not characteristically simple?

Published on 23 Feb 2026 - 2:16

score 85 · Answer 15 · 2026-02-23 02:08:22

85

Views

Why is $\langle r\rangle$ characteristic in $D_n$?

Published on 23 Feb 2026 - 2:08

List Question

Does there exist some sort of classification of finite "characteristically simple" groups?

Find all characteristic subgroups of the Dihedral group $D_{12}$.

Is there a common notation for characteristic subgroups?

If $G$ is a product of subnormal $S$ and a $p$-group, does the $p$-group need to be normal to know $\mathbf{O}^p(G) = \mathbf{O}^p(S)$?

Characteristic subgroups and factorization

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

Why do Automorphisms map maximal subgroups to maximal subgroups?

Proving Characteristic Subgroups are Transitive

Behaviour of restrictions of automorphisms of groups on characteristic subgroup under epimorphisms

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

Does there exist a verbally simple group, which is not characteristically simple?

Group $N \triangleleft G$, $(|N|,|G/N|) = 1$, then $N$ is a characteristic subgroup of $G$.

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

Does there exist an Artinian verbally simple group, which is not characteristically simple?

Why is $\langle r\rangle$ characteristic in $D_n$?

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