Question

Multiplication in $S_4$ with cycle notation and permutation matrices

score 120 · Answer 1 · 2026-03-26 16:03:54

120

Views

Multiplication in $S_4$ with cycle notation and permutation matrices

Published on 26 Mar 2026 - 16:03

score 35 · Answer 2 · 2022-09-02 22:09:50

35

Views

Show that $C_{S_{n}}(\sigma) \subset A_n$ if and only if the descomposition in disjoint cycles of $\sigma$ contains all most $1$ cycles of odd length

Published on 02 Sep 2022 - 22:09

score 249 · Answer 3 · 2026-04-05 21:49:08

249

Views

How many homomorphism are there of the form $S_n \to \mathbb{Z_2},n\geq 5$?

Published on 05 Apr 2026 - 21:49

score 97 · Answer 4 · 2026-04-08 19:52:49

97

Views

What's the meaning of setting a power symmetric polynomial to a given value

Published on 08 Apr 2026 - 19:52

score 113 · Answer 5 · 2026-03-28 02:06:39

113

Views

How many elements of the form $a^{m_1} b^{n_1} a^{m_2} b^{n_2} a^{m_3} b^{n_3}$ in $G:=\langle a,b \mid a^2, b^4, (ab)^3 \rangle?$

Published on 28 Mar 2026 - 2:06

score 88 · Answer 6 · 2022-09-09 04:45:11

88

Views

Find the number of abelian subgroups with order $15$ in symmetric group of degree $8$.

Published on 09 Sep 2022 - 4:45

score 78 · Answer 7 · 2026-03-21 04:15:24

78

Views

Decomposing $Sym^2\mathbb{C}[X]$ without using characters

Published on 21 Mar 2026 - 4:15

score 96 · Answer 8 · 2022-09-13 12:50:38

96

Views

Is this a correct way to factorise the symmetric group?

Published on 13 Sep 2022 - 12:50

score 52 · Answer 9 · 2022-09-13 16:45:30

52

Views

Verify/prove recursive expression involving sums over permutations and their signs

Published on 13 Sep 2022 - 16:45

score 65 · Answer 10 · 2026-04-08 19:35:57

65

Views

Showing that sign function sends transposition to $-1$.

Published on 08 Apr 2026 - 19:35

score 67 · Answer 11 · 2026-04-08 15:18:54

67

Views

Understanding a monoid ring through example

Published on 08 Apr 2026 - 15:18

score 58 · Answer 12 · 2022-09-16 20:44:32

58

Views

Compute $H=\{\rho^3_0,\rho^3_1,\rho^3_2, \mu^3_0,\mu^3_1,\mu^3_2\}$ and show that $H$ is not a subgroup of $S_3$.

Published on 16 Sep 2022 - 20:44

score 26 · Answer 13 · 2026-03-28 12:34:08

26

Views

all permutations of order 3

Published on 28 Mar 2026 - 12:34

score 136 · Answer 14 · 2022-09-21 23:05:39

136

Views

For any finite group $G$ of order $n$ show that there exists two subgroups $H_1, H_2 \leq S_n$ isomorphic to $G$ with $h_1h_2 = h_2h_1$

Published on 21 Sep 2022 - 23:05

score 172 · Answer 15 · 2026-03-30 15:31:20

172

Views

The character of the alternating sum of the exterior powers of the standard representation

Published on 30 Mar 2026 - 15:31

List Question

Multiplication in $S_4$ with cycle notation and permutation matrices

Show that $C_{S_{n}}(\sigma) \subset A_n$ if and only if the descomposition in disjoint cycles of $\sigma$ contains all most $1$ cycles of odd length

How many homomorphism are there of the form $S_n \to \mathbb{Z_2},n\geq 5$?

What's the meaning of setting a power symmetric polynomial to a given value

How many elements of the form $a^{m_1} b^{n_1} a^{m_2} b^{n_2} a^{m_3} b^{n_3}$ in $G:=\langle a,b \mid a^2, b^4, (ab)^3 \rangle?$

Find the number of abelian subgroups with order $15$ in symmetric group of degree $8$.

Decomposing $Sym^2\mathbb{C}[X]$ without using characters

Is this a correct way to factorise the symmetric group?

Verify/prove recursive expression involving sums over permutations and their signs

Showing that sign function sends transposition to $-1$.

Understanding a monoid ring through example

Compute $H=\{\rho^3_0,\rho^3_1,\rho^3_2, \mu^3_0,\mu^3_1,\mu^3_2\}$ and show that $H$ is not a subgroup of $S_3$.

all permutations of order 3

For any finite group $G$ of order $n$ show that there exists two subgroups $H_1, H_2 \leq S_n$ isomorphic to $G$ with $h_1h_2 = h_2h_1$

The character of the alternating sum of the exterior powers of the standard representation

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