List questions from symmetric-groups

Published on 29 Mar 2026 - 3:22

121

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Power of $ 2 $ congruent to 1 mod n

Published on 07 Aug 2022 - 17:30

71

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Solve the equation $a \circ x \circ b = c$ in the group $S_4$

Published on 08 Aug 2022 - 18:31

52

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How to show certain subgroups of $S_p$ are simple?

Published on 29 Mar 2026 - 3:12

166

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Group action for signal

Published on 12 Aug 2022 - 7:48

183

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Is there a conceptual proof that $A_n$ is simple for $n \ge 5$, or that it is the only nontrivial normal subgroup of $S_n$?

Published on 13 Aug 2022 - 6:44

52

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Show that the set $H=\{f \in S_4 \mid f(4)=4\} \subset S_4$ is isomorphic with $S_3$.

Published on 15 Aug 2022 - 16:09

255

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Equivalent definitions of a group acting on a group?

Published on 18 Aug 2022 - 11:07

71

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About $\text{Sym}(G) \setminus \text{Aut}(G)$

Published on 02 Apr 2026 - 2:54

64

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Why aren't there any $S_8$ or $S_{12}$ point groups in crystallography?

Published on 23 Feb 2026 - 2:40

83

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Let $G$ be a simple group, $H\leq G,[G:H]=n$ Prove $G \cong K,K\leq{\rm Sym}(n)$.

Published on 29 Mar 2026 - 3:36

72

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Generating function from symmetric group and combinatorics

Published on 28 Mar 2026 - 10:54

81

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Schur functors applied to irreducible representations of $S_n$

Published on 26 Mar 2026 - 4:14

137

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Use the idea of stacking diagrams to show that $S_n$ is generated by $\{(i \text{ } i+1):1\leq i \leq n-1\}$

Published on 29 Mar 2026 - 19:14

213

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Find all group homomorphisms $f: \Bbb Z_6 \to S_3$.

Published on 05 Apr 2026 - 21:48

List Question

Simple group order $168$ and $2$-transitive permutation subgroup of $S_7$

Power of $ 2 $ congruent to 1 mod n

Solve the equation $a \circ x \circ b = c$ in the group $S_4$

How to show certain subgroups of $S_p$ are simple?

Group action for signal

Is there a conceptual proof that $A_n$ is simple for $n \ge 5$, or that it is the only nontrivial normal subgroup of $S_n$?

Show that the set $H=\{f \in S_4 \mid f(4)=4\} \subset S_4$ is isomorphic with $S_3$.

Equivalent definitions of a group acting on a group?

About $\text{Sym}(G) \setminus \text{Aut}(G)$

Why aren't there any $S_8$ or $S_{12}$ point groups in crystallography?

Let $G$ be a simple group, $H\leq G,[G:H]=n$ Prove $G \cong K,K\leq{\rm Sym}(n)$.

Generating function from symmetric group and combinatorics

Schur functors applied to irreducible representations of $S_n$

Use the idea of stacking diagrams to show that $S_n$ is generated by $\{(i \text{ } i+1):1\leq i \leq n-1\}$

Find all group homomorphisms $f: \Bbb Z_6 \to S_3$.

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