List questions from symmetric-groups

Published on 19 Oct 2021 - 19:25

214

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How many elements of order 10 do exist in the group of permutations of 10 letters ($ S_{10}$)?

Published on 23 Oct 2021 - 20:24

86

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Learning representation of Lie algebras for someone who knows representations of the symmetric group

Published on 24 Oct 2021 - 18:31

457

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Does the symmetric group $S_{n+m}$ have a subgroup isomorphic to $S_n\times S_m$?

Published on 24 Oct 2021 - 21:02

205

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Sylow $2$-subgroup of $S_{2^n}$

Published on 27 Oct 2021 - 3:22

59

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Finding a specific basis to represent $S_3$

Published on 27 Oct 2021 - 12:59

24

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A question about higher order tensor notations and symmetric group action

Published on 28 Oct 2021 - 16:14

309

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Minimal degree faithful permutation representations of some finite simple groups

Published on 29 Oct 2021 - 5:23

104

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find a $\tau \in S_{8}$ such that $\tau\sigma \tau^{-1}=\sigma^{5}$

Published on 29 Oct 2021 - 13:36

21

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Scalars by which symmetrizations of cyclic permutations act on Specht modules

Published on 26 Mar 2026 - 4:30

327

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Prove that the group $S_4$ has exactly $4$ distinct subgroups of order $6$.

Published on 02 Nov 2021 - 8:49

130

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Determine all the homomorphisms $\varphi:\Bbb Z_4 \to S_3$.

Published on 04 Apr 2026 - 9:40

45

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Show that $\alpha^k\tau\alpha^{-k}=(k+1, k+2)$

Published on 28 Mar 2026 - 0:35

389

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How is a permutation composed of one cycle the product of disjoint cycles?

Published on 07 Nov 2021 - 3:09

58

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Given subgroup of $S_4$ how many cosets does it have?

Published on 07 Nov 2021 - 12:16

List Question

Show that multiplication in $S_n$ is noncommutative $\forall n \geq 3$

How many elements of order 10 do exist in the group of permutations of 10 letters ($ S_{10}$)?

Learning representation of Lie algebras for someone who knows representations of the symmetric group

Does the symmetric group $S_{n+m}$ have a subgroup isomorphic to $S_n\times S_m$?

Sylow $2$-subgroup of $S_{2^n}$

Finding a specific basis to represent $S_3$

A question about higher order tensor notations and symmetric group action

Minimal degree faithful permutation representations of some finite simple groups

find a $\tau \in S_{8}$ such that $\tau\sigma \tau^{-1}=\sigma^{5}$

Scalars by which symmetrizations of cyclic permutations act on Specht modules

Prove that the group $S_4$ has exactly $4$ distinct subgroups of order $6$.

Determine all the homomorphisms $\varphi:\Bbb Z_4 \to S_3$.

Show that $\alpha^k\tau\alpha^{-k}=(k+1, k+2)$

How is a permutation composed of one cycle the product of disjoint cycles?

Given subgroup of $S_4$ how many cosets does it have?

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