Question

If $n$ is odd, then the set of $n$-cycles consists of two conjugacy classes of equal size in $A_n$.

score 576 · Answer 1 · 2021-11-09 06:15:37

576

Views

If $n$ is odd, then the set of $n$-cycles consists of two conjugacy classes of equal size in $A_n$.

Published on 09 Nov 2021 - 6:15

score 106 · Answer 2 · 2021-11-10 16:26:56

106

Views

Characterization of symmetric group elements

Published on 10 Nov 2021 - 16:26

score 196 · Answer 3 · 2021-11-11 11:04:28

196

Views

Relation between two permutation metrics

Published on 11 Nov 2021 - 11:04

score 68 · Answer 4 · 2021-11-12 19:51:23

68

Views

Symmetric group elements with centralizer subgroups contained in alternating subgroup

Published on 12 Nov 2021 - 19:51

score 184 · Answer 5 · 2021-11-14 18:01:25

184

Views

Cardinality of a subset of $S_{p-1}$.

Published on 14 Nov 2021 - 18:01

score 125 · Answer 6 · 2026-04-04 11:25:38

125

Views

Homomorphism from $S_4$ to $S_6$

Published on 04 Apr 2026 - 11:25

score 431 · Answer 7 · 2026-03-28 02:05:22

431

Views

Finding number of permutations of order $k$ in $S_n$

Published on 28 Mar 2026 - 2:05

score 105 · Answer 8 · 2026-03-28 02:03:28

105

Views

What does the subgroup generated by a specific 3-cycle look like?

Published on 28 Mar 2026 - 2:03

score 18 · Answer 9 · 2026-02-23 03:26:55

18

Views

Metric functions induce clusters with infinite many points in each cluster

Published on 23 Feb 2026 - 3:26

score 38 · Answer 10 · 2021-11-20 18:30:48

38

Views

Let $x$ be $(1\dots n)\in S_n$ show that there exists $y\in x^{S_n}$ such that $x^{S_n} = x^{A_n}\sqcup y^{A_n}$.

Published on 20 Nov 2021 - 18:30

score 100 · Answer 11 · 2021-11-22 06:05:35

How does showing $\tau(i) = j \implies a\tau a^{-1}(a(i)) = a(j)$ demonstrate that $a\tau a^{-1}$ has the same cycle type as $\tau$?

score 25 · Answer 12 · 2021-11-23 00:33:12

25

Views

Order-theoretic restriction of a permutation

Published on 23 Nov 2021 - 0:33

score 73 · Answer 13 · 2021-11-23 02:42:00

73

Views

$S_3$ acting on a subgroup -- confirming my computation is correct

Published on 23 Nov 2021 - 2:42

score 233 · Answer 14 · 2021-11-24 22:38:55

233

Views

Why is the conjugacy class of an element in a symmetric group the same as the set of all elements with the same cycle type?

Published on 24 Nov 2021 - 22:38

score 204 · Answer 15 · 2026-03-29 10:18:15

204

Views

Show that there exists a monomorphism from $D_n$ to $S_n$.

Published on 29 Mar 2026 - 10:18

List Question

If $n$ is odd, then the set of $n$-cycles consists of two conjugacy classes of equal size in $A_n$.

Characterization of symmetric group elements

Relation between two permutation metrics

Symmetric group elements with centralizer subgroups contained in alternating subgroup

Cardinality of a subset of $S_{p-1}$.

Homomorphism from $S_4$ to $S_6$

Finding number of permutations of order $k$ in $S_n$

What does the subgroup generated by a specific 3-cycle look like?

Metric functions induce clusters with infinite many points in each cluster

Let $x$ be $(1\dots n)\in S_n$ show that there exists $y\in x^{S_n}$ such that $x^{S_n} = x^{A_n}\sqcup y^{A_n}$.

How does showing $\tau(i) = j \implies a\tau a^{-1}(a(i)) = a(j)$ demonstrate that $a\tau a^{-1}$ has the same cycle type as $\tau$?

Order-theoretic restriction of a permutation

$S_3$ acting on a subgroup -- confirming my computation is correct

Why is the conjugacy class of an element in a symmetric group the same as the set of all elements with the same cycle type?

Show that there exists a monomorphism from $D_n$ to $S_n$.

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