List questions from symmetric-groups

Published on 21 Dec 2023 - 7:45

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The standard representation of symmetry group

Published on 28 Dec 2023 - 6:53

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$S_n$ the symmetric group. Give an example of two elements $f,g$ of $S_n$ of order $2$ s.t. their product $f \circ g$ is of order $n$.

Published on 28 Dec 2023 - 17:35

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Basic question on showing transitivity on a finite set in $S_n$ ( symmetric group)

Published on 29 Dec 2023 - 18:43

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$G$ a finite group and let $p$ a prime divisor of $|G|$ prove that $G$ has an element of order $p$

Published on 03 Jan 2024 - 14:29

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$n \geq 5$, prove that the $3$-cycles of $A_n$ are pairwise conjugates in $A_n$. Is this true for $n=3$ or $n=4$?

Published on 05 Jan 2024 - 14:09

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Let $G$ be a normal non-trivial subgroup of $A_5$. Prove that $G=A_5$.

Published on 05 Jan 2024 - 18:10

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Let $f:G \rightarrow S_{G/H} $ the morphism induced by the action of $G$ by translation. Prove that $f(G)$ is not trivial.

Published on 06 Jan 2024 - 18:04

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Understanding proof of existence of cycle decomposition for $\sigma\in S_n$

Published on 12 Jan 2024 - 1:55

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The multiplicity of Specht modules

Published on 13 Jan 2024 - 14:31

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Restriction of induced representation over a Young subgroup and Littlewood-Richardson coefficients

Published on 20 Mar 2026 - 23:43

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Order of a Sylow $p$-subgroup of the symmetric group of order $p!$

Published on 29 Mar 2026 - 16:00

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A necessary condition for non-vanishing of irreducible characters of $S_n$

Published on 24 Jan 2024 - 20:35

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Is there a homomorphism $f: S_7 \to S_5$?

Published on 03 Feb 2024 - 13:24

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Fulton-Harris, Exercise 4.16

Published on 04 Feb 2024 - 2:31

List Question

Symmetries of PDEs

The standard representation of symmetry group

$S_n$ the symmetric group. Give an example of two elements $f,g$ of $S_n$ of order $2$ s.t. their product $f \circ g$ is of order $n$.

Basic question on showing transitivity on a finite set in $S_n$ ( symmetric group)

$G$ a finite group and let $p$ a prime divisor of $|G|$ prove that $G$ has an element of order $p$

$n \geq 5$, prove that the $3$-cycles of $A_n$ are pairwise conjugates in $A_n$. Is this true for $n=3$ or $n=4$?

Let $G$ be a normal non-trivial subgroup of $A_5$. Prove that $G=A_5$.

Let $f:G \rightarrow S_{G/H} $ the morphism induced by the action of $G$ by translation. Prove that $f(G)$ is not trivial.

Understanding proof of existence of cycle decomposition for $\sigma\in S_n$

The multiplicity of Specht modules

Restriction of induced representation over a Young subgroup and Littlewood-Richardson coefficients

Order of a Sylow $p$-subgroup of the symmetric group of order $p!$

A necessary condition for non-vanishing of irreducible characters of $S_n$

Is there a homomorphism $f: S_7 \to S_5$?

Fulton-Harris, Exercise 4.16

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