Question

Determine order of $\langle(12345),(2354)\rangle$.

score 96 · Answer 1 · 2022-01-07 10:40:47

96

Views

Determine order of $\langle(12345),(2354)\rangle$.

Published on 07 Jan 2022 - 10:40

score 79 · Answer 2 · 2026-03-31 10:39:12

79

Views

Is the continuous part of the symmetry group of a compact subset $\mathbb{R}^3$ isomorphic to $SO(k)$?

Published on 31 Mar 2026 - 10:39

score 89 · Answer 3 · 2026-03-28 03:55:27

89

Views

The evenness or oddness of the number of transpositions is determined only by the permutation. (In "Linear Algebra" by Ichiro Satake.)

Published on 28 Mar 2026 - 3:55

score 51 · Answer 4 · 2026-03-28 03:56:12

51

Views

Find all the permutations $ \tau $ such that $ \tau(1)=1 $

Published on 28 Mar 2026 - 3:56

score 179 · Answer 5 · 2026-03-30 08:58:30

179

Views

Explicit construction of induced character from cyclic subgroup of symmetric group

Published on 30 Mar 2026 - 8:58

score 152 · Answer 6 · 2022-01-15 02:46:51

152

Views

Which group do you get by taking the ultraproduct on the finite symmetric groups (given a fixed non-principal ultrafilter U)?

Published on 15 Jan 2022 - 2:46

score 179 · Answer 7 · 2026-03-26 04:14:47

179

Views

Are idempotents in the group algebra of $S_n$ equivalent to Specht modules?

Published on 26 Mar 2026 - 4:14

score 37 · Answer 8 · 2022-01-19 12:15:02

37

Views

For a finite $G$ group and $f_g(x) = gx$, if the permutation $\pi(f_g)$ defines the values of $f_g$, then is $\pi(f_{gh})=\pi(f_g)\pi(f_h)$?

Published on 19 Jan 2022 - 12:15

score 127 · Answer 9 · 2026-03-31 10:39:11

127

Views

Which rotation groups of compact subsets of $\mathbb{R}^n$ are symmetry groups of compact subsets of $\mathbb{R}^n$?

Published on 31 Mar 2026 - 10:39

score 62 · Answer 10 · 2026-03-28 03:56:14

62

Views

What's the process to calculate symmetric group multiplication

Published on 28 Mar 2026 - 3:56

score 35 · Answer 11 · 2026-03-28 06:40:38

35

Views

Computation of the derived series $S_3$ and show that it is solvable

Published on 28 Mar 2026 - 6:40

score 91 · Answer 12 · 2026-03-30 00:05:32

91

Views

Counting the size of a supposed presentation of $S_4$

Published on 30 Mar 2026 - 0:05

score 146 · Answer 13 · 2026-04-01 16:45:35

146

Views

Please tell me how to formalize my thought if my thought is not wrong. ("obvious by symmetry", "symmetric group")

Published on 01 Apr 2026 - 16:45

score 110 · Answer 14 · 2022-01-30 01:56:08

110

Views

If $f\in{\rm Aut}(S_3)$, prove there exists $\sigma\in S_3$ s.t. $f(\tau)=\sigma\tau\sigma^{-1}$ for every $\tau\in S_3$

Published on 30 Jan 2022 - 1:56

score 42 · Answer 15 · 2022-01-31 15:24:23

42

Views

Normal endomorphisms on $S_{n}$

Published on 31 Jan 2022 - 15:24

List Question

Determine order of $\langle(12345),(2354)\rangle$.

Is the continuous part of the symmetry group of a compact subset $\mathbb{R}^3$ isomorphic to $SO(k)$?

The evenness or oddness of the number of transpositions is determined only by the permutation. (In "Linear Algebra" by Ichiro Satake.)

Find all the permutations $ \tau $ such that $ \tau(1)=1 $

Explicit construction of induced character from cyclic subgroup of symmetric group

Which group do you get by taking the ultraproduct on the finite symmetric groups (given a fixed non-principal ultrafilter U)?

Are idempotents in the group algebra of $S_n$ equivalent to Specht modules?

For a finite $G$ group and $f_g(x) = gx$, if the permutation $\pi(f_g)$ defines the values of $f_g$, then is $\pi(f_{gh})=\pi(f_g)\pi(f_h)$?

Which rotation groups of compact subsets of $\mathbb{R}^n$ are symmetry groups of compact subsets of $\mathbb{R}^n$?

What's the process to calculate symmetric group multiplication

Computation of the derived series $S_3$ and show that it is solvable

Counting the size of a supposed presentation of $S_4$

Please tell me how to formalize my thought if my thought is not wrong. ("obvious by symmetry", "symmetric group")

If $f\in{\rm Aut}(S_3)$, prove there exists $\sigma\in S_3$ s.t. $f(\tau)=\sigma\tau\sigma^{-1}$ for every $\tau\in S_3$

Normal endomorphisms on $S_{n}$

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