Question

If $G$ embeds isomorphically into $\operatorname{Aut}(G)$ does that imply $Z(G) = \{1\}$?

score 73 · Answer 1 · 2026-03-25 09:28:36

73

Views

If $G$ embeds isomorphically into $\operatorname{Aut}(G)$ does that imply $Z(G) = \{1\}$?

Published on 25 Mar 2026 - 9:28

score 64 · Answer 2 · 2018-03-28 14:41:12

64

Views

Proof of a theorem of Galois in Endliche Gruppen I by Huppert

Published on 28 Mar 2018 - 14:41

score 36 · Answer 3 · 2026-03-25 01:17:37

36

Views

Reducedness of a factor ring in regard of group rings

Published on 25 Mar 2026 - 1:17

score 45 · Answer 4 · 2018-03-29 03:04:55

45

Views

Notation question for finite simple groups

Published on 29 Mar 2018 - 3:04

score 125 · Answer 5 · 2026-03-24 23:50:57

125

Views

Does Frattini argument hold for subnormal subgroup?

Published on 24 Mar 2026 - 23:50

score 175 · Answer 6 · 2026-03-25 17:39:33

175

Views

Is a subnormal Hall subgroup of a finite group normal?

Published on 25 Mar 2026 - 17:39

score 69 · Answer 7 · 2018-03-29 17:59:45

69

Views

Subgroup of order $n$ of $GL_n(\mathbb{F}_q)$

Published on 29 Mar 2018 - 17:59

score 117 · Answer 8 · 2026-03-25 09:36:59

117

Views

Is the following claim correct in general?

Published on 25 Mar 2026 - 9:36

score 41 · Answer 9 · 2018-03-30 16:08:36

41

Views

Is this a valid proof of equivalence of definitions of normal subgroup?

Published on 30 Mar 2018 - 16:08

score 1k · Answer 10 · 2026-03-24 22:07:39

1k

Views

What is the way to find the symmetry group of a set of points?

Published on 24 Mar 2026 - 22:07

score 319 · Answer 11 · 2018-03-31 15:12:09

319

Views

Irreducible decomposition of standard complex representation of an alternating group

Published on 31 Mar 2018 - 15:12

score 88 · Answer 12 · 2018-03-31 17:32:06

88

Views

Show $Z_{ab}\simeq Z_a\oplus Z_b$ by elementary row and column operations

Published on 31 Mar 2018 - 17:32

score 169 · Answer 13 · 2018-04-01 00:06:34

169

Views

Given a subgroup $H $, find a normal subgroup of $G$ with index less than or equal to $n!$

Published on 01 Apr 2018 - 0:06

score 87 · Answer 14 · 2018-04-02 01:55:29

87

Views

For every non-identity g∈G, there is exactly one element of S fixed by g. Prove that |S|mod k = 1.

Published on 02 Apr 2018 - 1:55

score 618 · Answer 15 · 2018-04-02 13:21:15

618

Views

Simplicity of rotational symmetry group of dodecahedron without proving it is $A_5$

Published on 02 Apr 2018 - 13:21

List Question

If $G$ embeds isomorphically into $\operatorname{Aut}(G)$ does that imply $Z(G) = \{1\}$?

Proof of a theorem of Galois in Endliche Gruppen I by Huppert

Reducedness of a factor ring in regard of group rings

Notation question for finite simple groups

Does Frattini argument hold for subnormal subgroup?

Is a subnormal Hall subgroup of a finite group normal?

Subgroup of order $n$ of $GL_n(\mathbb{F}_q)$

Is the following claim correct in general?

Is this a valid proof of equivalence of definitions of normal subgroup?

What is the way to find the symmetry group of a set of points?

Irreducible decomposition of standard complex representation of an alternating group

Show $Z_{ab}\simeq Z_a\oplus Z_b$ by elementary row and column operations

Given a subgroup $H $, find a normal subgroup of $G$ with index less than or equal to $n!$

For every non-identity g∈G, there is exactly one element of S fixed by g. Prove that |S|mod k = 1.

Simplicity of rotational symmetry group of dodecahedron without proving it is $A_5$

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