Question

Verify proof: Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.

score 119 · Answer 1 · 2022-10-26 23:53:00

119

Views

Verify proof: Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.

Published on 26 Oct 2022 - 23:53

score 54 · Answer 2 · 2026-04-08 22:33:25

54

Views

Issue with definitions for conjugacy classes.

Published on 08 Apr 2026 - 22:33

score 39 · Answer 3 · 2022-11-14 12:20:40

39

Views

Find the number of elements of $A_4$ composed of the product of two non-disjoint transpositions.

Published on 14 Nov 2022 - 12:20

score 30 · Answer 4 · 2026-03-29 18:11:10

30

Views

Show that for even integers $ n $ there exists an element $ g \in D_{n} $ : $ \operatorname{ord}(g)=2 $ and $ \operatorname{sgn}(\varphi(g))=1 $

Published on 29 Mar 2026 - 18:11

score 27 · Answer 5 · 2026-03-26 04:13:32

27

Views

Linear involution for Specht modules

Published on 26 Mar 2026 - 4:13

score 115 · Answer 6 · 2026-04-07 06:38:40

115

Views

Symmetric vector least squares solution

Published on 07 Apr 2026 - 6:38

score 41 · Answer 7 · 2022-11-19 22:35:51

41

Views

Extending the hamming distance on Sym$(X)$ to linear groups

Published on 19 Nov 2022 - 22:35

score 133 · Answer 8 · 2026-04-01 11:59:32

133

Views

Product of Permutation Representation Characters

Published on 01 Apr 2026 - 11:59

score 55 · Answer 9 · 2022-11-29 21:15:40

55

Views

Is there any nonabelian group of order $n$ that isn't a subgroup of $S_{n-1}$?

Published on 29 Nov 2022 - 21:15

score 85 · Answer 10 · 2022-11-30 07:01:12

85

Views

transitive subgroups in $S_n$ that are isomorphic to $S_k$ for $k\leq n$

Published on 30 Nov 2022 - 7:01

score 115 · Answer 11 · 2022-11-30 15:53:38

115

Views

Show $\phi : S_3 \rightarrow S_3$ given by $\phi(f^{i}g^{j}) = f^{2i}g^{j}$ is an automorphism

Published on 30 Nov 2022 - 15:53

score 136 · Answer 12 · 2022-12-05 04:33:30

136

Views

Prove $\operatorname{sgn}(\pi) = (-1)^r$ where $r$ is the number of inversions.

Published on 05 Dec 2022 - 4:33

score 154 · Answer 13 · 2022-12-05 18:21:53

154

Views

Subgroup Requirements

Published on 05 Dec 2022 - 18:21

score 150 · Answer 14 · 2022-12-08 11:35:55

150

Views

Let $H = \{g \in S_6 : g(a)\equiv a\pmod3 \text{ for } a\in\{1,2,3,4,5,6\}\}.$ Is this a subgroup?

Published on 08 Dec 2022 - 11:35

score 183 · Answer 15 · 2026-03-28 16:19:59

183

Views

Unique representation of a graph (graph automorphism) in python

Published on 28 Mar 2026 - 16:19

List Question

Verify proof: Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.

Issue with definitions for conjugacy classes.

Find the number of elements of $A_4$ composed of the product of two non-disjoint transpositions.

Show that for even integers $ n $ there exists an element $ g \in D_{n} $ : $ \operatorname{ord}(g)=2 $ and $ \operatorname{sgn}(\varphi(g))=1 $

Linear involution for Specht modules

Symmetric vector least squares solution

Extending the hamming distance on Sym$(X)$ to linear groups

Product of Permutation Representation Characters

Is there any nonabelian group of order $n$ that isn't a subgroup of $S_{n-1}$?

transitive subgroups in $S_n$ that are isomorphic to $S_k$ for $k\leq n$

Show $\phi : S_3 \rightarrow S_3$ given by $\phi(f^{i}g^{j}) = f^{2i}g^{j}$ is an automorphism

Prove $\operatorname{sgn}(\pi) = (-1)^r$ where $r$ is the number of inversions.

Subgroup Requirements

Let $H = \{g \in S_6 : g(a)\equiv a\pmod3 \text{ for } a\in\{1,2,3,4,5,6\}\}.$ Is this a subgroup?

Unique representation of a graph (graph automorphism) in python

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