List questions from symmetric-groups

Published on 06 Jun 2022 - 5:34

94

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Prove $\{\sigma\in S_\Bbb N\mid\sigma(x)= x\text{ for all but finitely many }x\in\Bbb{N}\}$ is not finitely generated

Published on 06 Jun 2022 - 11:32

81

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Are there two isomorphic transitive subgroups of $\mathfrak{S}_n$ that are not conjugate?

Published on 25 Mar 2026 - 8:10

173

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Average number of the maximum amount of fixed points of permutation in a partition of $S_n$

Published on 28 Mar 2026 - 7:41

43

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Is any $S_4$-invariant function also $S_6$ invariant?

Published on 27 Mar 2026 - 3:57

71

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Schur's orthogonality relations on the symmetric Group $S_3$

Published on 14 Jun 2022 - 9:48

126

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Why is $[S_n:K]=2$ and $A_nK=S_n$ a contradiction?

Published on 15 Jun 2022 - 21:40

172

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Find a larger degree permutation representation

Published on 16 Jun 2022 - 23:27

77

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Let $H = \{\alpha^2 : \alpha \in S_4\}$. Show that $H = A_4$.

Published on 18 Jun 2022 - 2:01

39

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Output of composition $\delta_2(\rho_3(1234))$ in $D_4$.

Published on 19 Jun 2022 - 14:21

123

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Random generators of the symmetric group $S_n$

Published on 19 Jun 2022 - 20:50

103

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Find the order of the following elements in ${\rm Inn}(S_5)$

Published on 02 Apr 2026 - 1:02

40

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The elements which when multiplied give us conjugation with respect to three cycles

Published on 28 Jun 2022 - 11:58

250

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Find the smallest $n$ such that $S_n$ has an element of given order.

Published on 02 Jul 2022 - 11:57

51

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$S_n$ relation between vertices in cycle and group order.

Published on 02 Jul 2022 - 16:23

List Question

Transitive group actions and transitive subgroups

Prove $\{\sigma\in S_\Bbb N\mid\sigma(x)= x\text{ for all but finitely many }x\in\Bbb{N}\}$ is not finitely generated

Are there two isomorphic transitive subgroups of $\mathfrak{S}_n$ that are not conjugate?

Average number of the maximum amount of fixed points of permutation in a partition of $S_n$

Is any $S_4$-invariant function also $S_6$ invariant?

Schur's orthogonality relations on the symmetric Group $S_3$

Why is $[S_n:K]=2$ and $A_nK=S_n$ a contradiction?

Find a larger degree permutation representation

Let $H = \{\alpha^2 : \alpha \in S_4\}$. Show that $H = A_4$.

Output of composition $\delta_2(\rho_3(1234))$ in $D_4$.

Random generators of the symmetric group $S_n$

Find the order of the following elements in ${\rm Inn}(S_5)$

The elements which when multiplied give us conjugation with respect to three cycles

Find the smallest $n$ such that $S_n$ has an element of given order.

$S_n$ relation between vertices in cycle and group order.

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