List questions from symmetric-groups

Published on 13 Feb 2017 - 16:56

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Doubly transitive subgroup of $S_n$

Published on 14 Feb 2017 - 3:22

734

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Subgroup generated by two permutations

Published on 15 Feb 2017 - 0:23

355

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Confusing notation: Presentation theory of symmetric groups (Coxeter presentations)

Published on 25 Mar 2026 - 14:21

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If R and S are both anti-symmetric, then R ∪ S is anti-symmetric

Published on 18 Feb 2017 - 20:22

190

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Let $K=\{ (1), (12)(34),(13)(24),(14)(23)\}$ and let $G=S_4$. Determine whether the following classes are disjoint or identical

Published on 22 Feb 2017 - 1:03

612

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The "fake $\mathrm{GL}_2(\mathbb{F}_3)$" and the binary octahedral group

Published on 25 Mar 2026 - 3:22

33

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Find $\pi \in S_9$ such that $\pi \circ (4,5,6,8) = (1,7,6,8,9)(2,3)$.

Published on 23 Feb 2017 - 8:41

119

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Prove that if $α ∈ S_n$ is an $m$-cycle, then $α$ is a product of transpositions.

Published on 26 Feb 2017 - 1:17

48

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Rules associated with disjoint cycle operations

Published on 26 Feb 2017 - 18:56

911

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cycle index of symmetric group: sanity check

Published on 27 Mar 2026 - 15:36

197

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Is a vector space a subset of an abelian group?

Published on 27 Feb 2017 - 22:47

235

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Will the two elements in $S_n$ have the same cycle structure?

Published on 01 Mar 2017 - 2:23

158

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$S_3$ permutes the elements of $\mathbb{R}^3$, show that $\sigma (x_1, x_2, x_3) = ( x_{\sigma^{-1}(1)}, x_{\sigma^{-1}(2)}, x_{\sigma^{-1}(3)})$.

Published on 01 Mar 2017 - 4:29

78

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symmetric group, eigeproblem

Published on 02 Mar 2017 - 11:12

List Question

Identify irreducible representations of $A_4$

Doubly transitive subgroup of $S_n$

Subgroup generated by two permutations

Confusing notation: Presentation theory of symmetric groups (Coxeter presentations)

If R and S are both anti-symmetric, then R ∪ S is anti-symmetric

Let $K=\{ (1), (12)(34),(13)(24),(14)(23)\}$ and let $G=S_4$. Determine whether the following classes are disjoint or identical

The "fake $\mathrm{GL}_2(\mathbb{F}_3)$" and the binary octahedral group

Find $\pi \in S_9$ such that $\pi \circ (4,5,6,8) = (1,7,6,8,9)(2,3)$.

Prove that if $α ∈ S_n$ is an $m$-cycle, then $α$ is a product of transpositions.

Rules associated with disjoint cycle operations

cycle index of symmetric group: sanity check

Is a vector space a subset of an abelian group?

Will the two elements in $S_n$ have the same cycle structure?

$S_3$ permutes the elements of $\mathbb{R}^3$, show that $\sigma (x_1, x_2, x_3) = ( x_{\sigma^{-1}(1)}, x_{\sigma^{-1}(2)}, x_{\sigma^{-1}(3)})$.

symmetric group, eigeproblem

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