List questions from symmetric-groups

Published on 05 Sep 2017 - 2:17

524

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For what values of k the action is faithful?

Published on 08 Sep 2017 - 13:25

94

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Murnaghan-Nakayama rule for general dimension of a hook

Published on 25 Mar 2026 - 20:13

159

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Show that if $(\sigma^r)^i$ is an $n$-cycle, then $\sigma^r$ is an $n$-cycle

Published on 15 Sep 2017 - 21:04

26

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Suppose that $(S_n, \circ)$ is a symmetric group with $n \geq 3$, then a permutation of $(i,j)=(1,i)(1,j)(1,i)$

Published on 16 Sep 2017 - 20:26

715

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Prove that the only way $S_3$ can act transitively on a set of order 3 is by giving the permutations of the set

Published on 19 Sep 2017 - 7:38

1.8k

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Show that every subgroup of $S_n$ has either every member as even or exactly half the members as even permutations.

Published on 20 Sep 2017 - 5:58

151

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Systematic way to find all automorphisms of a (particular) symmetric group?

Published on 24 Sep 2017 - 10:21

173

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Prove that $\tau (x_1 x_2 ... x_k) \tau^{-1} = (\tau(x_1) \tau(x_2) ... \tau (x_k))$

Published on 24 Sep 2017 - 12:38

112

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Show that $H=A_n$

Published on 24 Sep 2017 - 17:20

1.8k

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Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$

Published on 28 Sep 2017 - 13:03

26

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How do I prove that an element or multiple elements are in both H and K?

Published on 29 Sep 2017 - 6:22

31

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Show that $G \cong D_4$.

Published on 30 Mar 2026 - 23:02

789

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Subgroup of all self inverse elements

Published on 05 Oct 2017 - 7:51

211

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Find an element $g\in S_6$ such that $g(123)(456)g^{-1}=(531)(264)$.

Published on 07 Oct 2017 - 8:14

List Question

Computation in a Permutation Group

For what values of k the action is faithful?

Murnaghan-Nakayama rule for general dimension of a hook

Show that if $(\sigma^r)^i$ is an $n$-cycle, then $\sigma^r$ is an $n$-cycle

Suppose that $(S_n, \circ)$ is a symmetric group with $n \geq 3$, then a permutation of $(i,j)=(1,i)(1,j)(1,i)$

Prove that the only way $S_3$ can act transitively on a set of order 3 is by giving the permutations of the set

Show that every subgroup of $S_n$ has either every member as even or exactly half the members as even permutations.

Systematic way to find all automorphisms of a (particular) symmetric group?

Prove that $\tau (x_1 x_2 ... x_k) \tau^{-1} = (\tau(x_1) \tau(x_2) ... \tau (x_k))$

Show that $H=A_n$

Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$

How do I prove that an element or multiple elements are in both H and K?

Show that $G \cong D_4$.

Subgroup of all self inverse elements

Find an element $g\in S_6$ such that $g(123)(456)g^{-1}=(531)(264)$.

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