List questions from symmetric-groups

Published on 27 Oct 2018 - 10:32

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Types of group action observing the table of $G$ acting in $X$

Published on 25 Mar 2026 - 20:36

246

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Show that $σ(1\, 2\, 3\, 4 ...... k)σ^{−1}=(σ(1)\,σ(2)…σ(k))$, where $(σ(1)\,σ(2)…σ(k))$ is another k-cycle.

Published on 28 Oct 2018 - 19:19

3.7k

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How many cycles of each type are in $S_6$

Published on 29 Oct 2018 - 2:58

526

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Centraliser of (12)(34) in A5

Published on 29 Oct 2018 - 20:20

139

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$Hol(\Bbb Z_2 \times \Bbb Z_2)$

Published on 31 Oct 2018 - 3:19

1.8k

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Why are there 48 symmetries of a cube?

Published on 31 Oct 2018 - 16:07

210

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Prove that $S_4 \cong V_4 \rtimes_\phi S_3$ for any isomorphism $\phi: S_3 \to \text{Aut}(V_4)$

Published on 25 Mar 2026 - 6:04

106

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Conjugacy in Galois group and in symmetric group

Published on 05 Nov 2018 - 14:46

39

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A question on $G=S_5$ concerning notation

Published on 06 Nov 2018 - 20:11

209

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Is this proof on the Sylow 5-subgroups of G 100% correct?

Published on 25 Mar 2026 - 9:38

91

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Generating Symmetric Group from a subset

Published on 07 Nov 2018 - 6:33

612

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Prove that the alternating group $A_{n}$ is generated by all products of two 2-cycles.

Published on 07 Nov 2018 - 16:40

190

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The automorphism group of $S_6$ is isomorphic to a semidirect prodct

Published on 25 Mar 2026 - 15:51

477

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Group homomorphism from $A_n$ to $C^*$

Published on 11 Nov 2018 - 14:14

List Question

Confusion on Irreducible representations of a group

Types of group action observing the table of $G$ acting in $X$

Show that $σ(1\, 2\, 3\, 4 ...... k)σ^{−1}=(σ(1)\,σ(2)…σ(k))$, where $(σ(1)\,σ(2)…σ(k))$ is another k-cycle.

How many cycles of each type are in $S_6$

Centraliser of (12)(34) in A5

$Hol(\Bbb Z_2 \times \Bbb Z_2)$

Why are there 48 symmetries of a cube?

Prove that $S_4 \cong V_4 \rtimes_\phi S_3$ for any isomorphism $\phi: S_3 \to \text{Aut}(V_4)$

Conjugacy in Galois group and in symmetric group

A question on $G=S_5$ concerning notation

Is this proof on the Sylow 5-subgroups of G 100% correct?

Generating Symmetric Group from a subset

Prove that the alternating group $A_{n}$ is generated by all products of two 2-cycles.

The automorphism group of $S_6$ is isomorphic to a semidirect prodct

Group homomorphism from $A_n$ to $C^*$

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