List questions from symmetric-groups

Published on 25 Mar 2026 - 6:03

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Finding the centraliser of an element in $S_5$

Published on 01 Dec 2018 - 19:20

184

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Constructing a particular transitive subgroup

Published on 05 Dec 2018 - 22:31

557

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Show that $\phi(g)$ is an even permutation

Published on 06 Dec 2018 - 15:05

46

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Let $G=S_n$ and fix $i \in A=\{1,2,\ldots,n\}$ and let $G_{i}=\{\alpha \in G | \alpha(i)= i\}$. Prove $G_{i} \leq G$ and find $|G_i|$

Published on 26 Mar 2026 - 4:34

76

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Counting permutations in $S_n$ which take an n-cycle to another n-cycle under conjugation

Published on 07 Dec 2018 - 21:23

200

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Let $n$ be an odd positive integer and $a\in S_n$ be an $n$-cycle. Show that the order of $C(a)$ must be odd.

Published on 25 Mar 2026 - 6:06

593

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One of the conjugacy classes of A4

Published on 11 Dec 2018 - 6:03

46

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How to check if permutation induces an element of the Galois group.

Published on 11 Dec 2018 - 15:57

208

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Permutation groups: $S_4$ and $D_4$.

Published on 12 Dec 2018 - 2:26

43

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G has 4-Sylow 3-subgroups

Published on 25 Mar 2026 - 14:20

258

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Show that (12345) and (12) create $S_5$

Published on 13 Dec 2018 - 9:09

85

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Cycles and symmetric groups

Published on 20 Dec 2018 - 12:50

329

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What is the meaning of $\rho$ and $\sigma$ in the symmetric group?

Published on 21 Dec 2018 - 16:59

70

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Uniqueness of dimensions of irreps of $S_n$

Published on 21 Dec 2018 - 22:20

List Question

find all $x \in S_5$ such that $x^3 = (12)$

Finding the centraliser of an element in $S_5$

Constructing a particular transitive subgroup

Show that $\phi(g)$ is an even permutation

Let $G=S_n$ and fix $i \in A=\{1,2,\ldots,n\}$ and let $G_{i}=\{\alpha \in G | \alpha(i)= i\}$. Prove $G_{i} \leq G$ and find $|G_i|$

Counting permutations in $S_n$ which take an n-cycle to another n-cycle under conjugation

Let $n$ be an odd positive integer and $a\in S_n$ be an $n$-cycle. Show that the order of $C(a)$ must be odd.

One of the conjugacy classes of A4

How to check if permutation induces an element of the Galois group.

Permutation groups: $S_4$ and $D_4$.

G has 4-Sylow 3-subgroups

Show that (12345) and (12) create $S_5$

Cycles and symmetric groups

What is the meaning of $\rho$ and $\sigma$ in the symmetric group?

Uniqueness of dimensions of irreps of $S_n$

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