List questions from symmetric-groups

Published on 29 Mar 2026 - 4:11

349

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Indicate two nonconjugate isomorphic subgroups of order $12$ in $S_{11}$

Published on 02 Apr 2017 - 18:28

1.2k

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Writing every element of $S_n$ as a product of permutations of order 2

Published on 03 Apr 2017 - 19:27

42

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If $h$ is the $k$-cycle and g element of $S_n$, prove that $ghg^{-1}=(g(a_1)g(a_2)...g(a_k))$

Published on 04 Apr 2017 - 2:53

169

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How to find the numer of symmetries of a geometric figure

Published on 04 Apr 2017 - 8:10

634

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Determine a normal subgroup $N$ of $G$ and determine the multiplication table for $G/N$

Published on 04 Apr 2017 - 14:05

129

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Describe the reflections in an equilateral prism

Published on 04 Apr 2017 - 19:44

157

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For $\sigma=(1,2,\dots,n)\in S_n$, I need to show if $\tau\in S_n$ commutes with $\sigma$ then $\tau=\sigma^k$ for some $k\ge 1$.

Published on 08 Apr 2017 - 10:28

311

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Technics to find conjugacy classes of a symmetry group

Published on 08 Apr 2017 - 18:28

163

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Proof techniques to show a representation is faithful

Published on 25 Mar 2026 - 8:07

333

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What's the smallest $n$ for which $S_n$ has an element of order $30?$

Published on 26 Mar 2026 - 17:32

101

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Is the following presentation for $D_8$ a valid presentation?

Published on 26 Mar 2026 - 19:05

29

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Combining Operation for $S_4$

Published on 09 Feb 2023 - 8:51

222

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On the cyclicity of $\operatorname{Aut}(\Bbb Z/p\Bbb Z)$, for $p$ a prime.

Published on 29 Mar 2026 - 20:11

62

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$\Sigma\le S_n$ of order $n$. Is $\Sigma$ cyclic, if each $\tau\in\Sigma\setminus\{Id\}$ moves all the elements?

Published on 14 Feb 2023 - 17:22

List Question

Exercise on Sylow's theorems

Indicate two nonconjugate isomorphic subgroups of order $12$ in $S_{11}$

Writing every element of $S_n$ as a product of permutations of order 2

If $h$ is the $k$-cycle and g element of $S_n$, prove that $ghg^{-1}=(g(a_1)g(a_2)...g(a_k))$

How to find the numer of symmetries of a geometric figure

Determine a normal subgroup $N$ of $G$ and determine the multiplication table for $G/N$

Describe the reflections in an equilateral prism

For $\sigma=(1,2,\dots,n)\in S_n$, I need to show if $\tau\in S_n$ commutes with $\sigma$ then $\tau=\sigma^k$ for some $k\ge 1$.

Technics to find conjugacy classes of a symmetry group

Proof techniques to show a representation is faithful

What's the smallest $n$ for which $S_n$ has an element of order $30?$

Is the following presentation for $D_8$ a valid presentation?

Combining Operation for $S_4$

On the cyclicity of $\operatorname{Aut}(\Bbb Z/p\Bbb Z)$, for $p$ a prime.

$\Sigma\le S_n$ of order $n$. Is $\Sigma$ cyclic, if each $\tau\in\Sigma\setminus\{Id\}$ moves all the elements?

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