List questions from symmetric-groups

71

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Let $G$ be a non abelian simple group. Show that ${\rm Aut}(G^n)$ is isomorphic to ${\rm Aut}(G) \wr{\rm Sym}(n).$

Published on 25 Mar 2026 - 14:36

146

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Yes/No: There always exists an injective homomorphism from $G$ into $S_n$.

Published on 05 Apr 2026 - 7:19

322

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Symmetric Group of an amorphous set

Published on 19 Apr 2022 - 10:57

52

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Cayley's theorem - How many cycles of each type exists

Published on 20 Apr 2022 - 11:58

110

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Homomorphisms from $S_3$ to $\mathbb{Z}/10\mathbb{Z}$

Published on 05 Apr 2026 - 13:46

385

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$\sigma \in S_n$ does not commute with any odd permutation if and only if the cycle type of a consists of distinct odd integers.

Published on 27 Apr 2022 - 16:18

51

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Abelian group of order $pq$ is a subgroup of $S_{p+q}$

Published on 30 Apr 2022 - 21:32

213

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About a proof for $S_n$ being generated by adjacent transpositions

Published on 04 May 2022 - 1:11

122

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No Subgroup of $S_7$ of order 15

Published on 05 May 2022 - 0:31

137

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Representation of $\mathfrak{S}_p$ over $\mathbb{F}_p$

Published on 26 Mar 2026 - 19:17

14

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What transitive action of a permutation group connects the Prufer 2-group?

Published on 01 Mar 2026 - 17:08

215

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Is $S_2 \wr S_k$ contained in $(S_a \times S_b) \wr S_{k-1}$?

Published on 25 Mar 2026 - 14:36

90

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Proof idea: $S_3 \cong D_3$

Published on 29 Mar 2026 - 13:22

87

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Number of inversions in $S_n$

Published on 27 Mar 2026 - 4:38

28

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Signature of a permutation couple

Published on 16 May 2022 - 20:55

List Question

Let $G$ be a non abelian simple group. Show that ${\rm Aut}(G^n)$ is isomorphic to ${\rm Aut}(G) \wr{\rm Sym}(n).$

Yes/No: There always exists an injective homomorphism from $G$ into $S_n$.

Symmetric Group of an amorphous set

Cayley's theorem - How many cycles of each type exists

Homomorphisms from $S_3$ to $\mathbb{Z}/10\mathbb{Z}$

$\sigma \in S_n$ does not commute with any odd permutation if and only if the cycle type of a consists of distinct odd integers.

Abelian group of order $pq$ is a subgroup of $S_{p+q}$

About a proof for $S_n$ being generated by adjacent transpositions

No Subgroup of $S_7$ of order 15

Representation of $\mathfrak{S}_p$ over $\mathbb{F}_p$

What transitive action of a permutation group connects the Prufer 2-group?

Is $S_2 \wr S_k$ contained in $(S_a \times S_b) \wr S_{k-1}$?

Proof idea: $S_3 \cong D_3$

Number of inversions in $S_n$

Signature of a permutation couple

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