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In search of the most symmetric Steiner quadruple systems

score 112 · Answer 1 · 2026-03-26 19:03:06

112

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In search of the most symmetric Steiner quadruple systems

Published on 26 Mar 2026 - 19:03

score 351 · Answer 2 · 2022-02-05 01:21:29

351

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Please tell me what the author wants to say. ("Topics in Algebra 2nd Edition" by I N. Herstein)

Published on 05 Feb 2022 - 1:21

score 360 · Answer 3 · 2022-02-07 03:12:06

360

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Let $G$ be a finite group. Let $T$ be an element of $\operatorname{Aut}(G)$ such that $T^2=I$, and $xT=x\Leftrightarrow x=e$. Then, $G$ is abelian.

Published on 07 Feb 2022 - 3:12

score 101 · Answer 4 · 2026-04-01 11:21:18

101

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Prove that $n\mid\phi(a^n-1)$ in "Topics in Algebra 2nd Edition" by I. N. Herstein. Any natural solution that uses $\operatorname{Aut}(G)$?

Published on 01 Apr 2026 - 11:21

score 67 · Answer 5 · 2026-03-29 10:58:59

67

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$G$ is a group and $T\in\operatorname{Aut}(G)$. If $N\lhd G$ such that $(N)T\subset N$, show how you could use $T$ to define an automorphism of $G/N$.

Published on 29 Mar 2026 - 10:58

score 29 · Answer 6 · 2022-02-15 10:12:22

29

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Can you make every two isomorphic subgroups conjugated?

Published on 15 Feb 2022 - 10:12

score 90 · Answer 7 · 2022-02-18 13:25:33

90

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Abelianiness of a finite $G$ with an automorphism of order $2$ which doesn't fix any nontrivial element (alternative proof?).

Published on 18 Feb 2022 - 13:25

score 130 · Answer 8 · 2022-02-19 15:39:18

130

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Torsion-free Aut(G), but torsion in Out(G)

Published on 19 Feb 2022 - 15:39

score 21 · Answer 9 · 2022-02-22 19:35:14

21

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What's the purpose/motivation of defining inner automorphisms?

Published on 22 Feb 2022 - 19:35

score 76 · Answer 10 · 2026-03-28 13:27:25

76

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Sufficient condition for a non-empty intersection of two graph automorphism sets

Published on 28 Mar 2026 - 13:27

score 200 · Answer 11 · 2022-03-03 16:59:15

200

Views

Tiling of Klein quartic with 56 equilateral triangles

Published on 03 Mar 2022 - 16:59

score 321 · Answer 12 · 2022-03-04 18:16:22

321

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What does the Outer automorphism group act on? If an automorphism preserves conjugacy classes, is it inner?

Published on 04 Mar 2022 - 18:16

score 78 · Answer 13 · 2022-03-04 19:44:43

78

Views

Tricks to compute automorphism groups quickly

Published on 04 Mar 2022 - 19:44

score 186 · Answer 14 · 2022-03-07 16:19:23

186

Views

$\operatorname{Aut}_c(G)$ vs "$\operatorname{Inn}_c(G)$"

Published on 07 Mar 2022 - 16:19

score 91 · Answer 15 · 2022-03-07 21:06:59

91

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Galois group of $x^3-2$ over $\mathbb{Q}(\omega)$

Published on 07 Mar 2022 - 21:06

List Question

In search of the most symmetric Steiner quadruple systems

Please tell me what the author wants to say. ("Topics in Algebra 2nd Edition" by I N. Herstein)

Let $G$ be a finite group. Let $T$ be an element of $\operatorname{Aut}(G)$ such that $T^2=I$, and $xT=x\Leftrightarrow x=e$. Then, $G$ is abelian.

Prove that $n\mid\phi(a^n-1)$ in "Topics in Algebra 2nd Edition" by I. N. Herstein. Any natural solution that uses $\operatorname{Aut}(G)$?

$G$ is a group and $T\in\operatorname{Aut}(G)$. If $N\lhd G$ such that $(N)T\subset N$, show how you could use $T$ to define an automorphism of $G/N$.

Can you make every two isomorphic subgroups conjugated?

Abelianiness of a finite $G$ with an automorphism of order $2$ which doesn't fix any nontrivial element (alternative proof?).

Torsion-free Aut(G), but torsion in Out(G)

What's the purpose/motivation of defining inner automorphisms?

Sufficient condition for a non-empty intersection of two graph automorphism sets

Tiling of Klein quartic with 56 equilateral triangles

What does the Outer automorphism group act on? If an automorphism preserves conjugacy classes, is it inner?

Tricks to compute automorphism groups quickly

$\operatorname{Aut}_c(G)$ vs "$\operatorname{Inn}_c(G)$"

Galois group of $x^3-2$ over $\mathbb{Q}(\omega)$

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