Question

Every element of $S_n$ can be written as a product of transpositions of the form $(1 i )$, for various $i$

score 1.4k · Answer 1 · 2026-03-27 19:33:39

1.4k

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Every element of $S_n$ can be written as a product of transpositions of the form $(1 i )$, for various $i$

Published on 27 Mar 2026 - 19:33

score 184 · Answer 2 · 2021-05-19 16:31:51

184

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$A_n$ is simple if $n \ge 5$

Published on 19 May 2021 - 16:31

score 241 · Answer 3 · 2026-03-27 21:23:56

241

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In $S_7$, describe the conjugates of $(1 2)(3 4 5)$

Published on 27 Mar 2026 - 21:23

score 78 · Answer 4 · 2021-05-20 10:47:56

78

Views

Determine the less value of $n\in\mathbb{N}$ for $S_{n}$ having an element of order $200$

Published on 20 May 2021 - 10:47

score 45 · Answer 5 · 2026-03-25 23:42:20

45

Views

Does the product of two Schur functions always have a lattice structure with respect to the dominance order of partitions?

Published on 25 Mar 2026 - 23:42

score 58 · Answer 6 · 2026-03-26 02:34:56

58

Views

Computing permutation character associated to a Young subgroup.

Published on 26 Mar 2026 - 2:34

score 540 · Answer 7 · 2026-03-29 15:21:30

540

Views

Artin's presentation of $S_3$

Published on 29 Mar 2026 - 15:21

score 459 · Answer 8 · 2021-05-22 23:53:17

459

Views

How is the rotation symmetry group of the square rectangular cuboid isomorphic to the symmetry group of the square?

Published on 22 May 2021 - 23:53

score 389 · Answer 9 · 2021-05-25 16:01:50

389

Views

Let $p$ be a prime. Find a formula for the number of conjugacy classes of elements of order $p$ in $S_n$.

Published on 25 May 2021 - 16:01

score 90 · Answer 10 · 2026-03-28 00:30:56

90

Views

If $S$ is all finitary permutations of $\Bbb N$ and $A$ is the alternating subgroup, prove $1\lhd A\lhd S$ is the only composition series of $S$

Published on 28 Mar 2026 - 0:30

score 161 · Answer 11 · 2026-03-31 03:58:12

161

Views

Irreducibility of exterior powers of representations of the symmetric group over finite fields

Published on 31 Mar 2026 - 3:58

score 73 · Answer 12 · 2026-03-27 17:57:22

73

Views

Is the symmetric group over 8 items, $S_8$, presented by $\langle x, y \mid x^2 = e, y^8 = e, (xy)^7 = e \rangle$?

Published on 27 Mar 2026 - 17:57

score 82 · Answer 13 · 2026-03-27 19:33:38

82

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Prove that $\tau \sigma \tau ^{-1}$ depends only on the lateral class of $\tau$ with respect to $Z(\sigma)$

Published on 27 Mar 2026 - 19:33

score 374 · Answer 14 · 2026-04-04 01:54:39

374

Views

Artin's Algebra: Homomorphism $S_4 \to S_3$

Published on 04 Apr 2026 - 1:54

score 226 · Answer 15 · 2026-03-27 21:20:27

226

Views

Find the conjugacy class in $S_n$ of $(12...n)$. What is the order of the centalizer of $(12...n)$ in $S_n$?

Published on 27 Mar 2026 - 21:20

List Question

Every element of $S_n$ can be written as a product of transpositions of the form $(1 i )$, for various $i$

$A_n$ is simple if $n \ge 5$

In $S_7$, describe the conjugates of $(1 2)(3 4 5)$

Determine the less value of $n\in\mathbb{N}$ for $S_{n}$ having an element of order $200$

Does the product of two Schur functions always have a lattice structure with respect to the dominance order of partitions?

Computing permutation character associated to a Young subgroup.

Artin's presentation of $S_3$

How is the rotation symmetry group of the square rectangular cuboid isomorphic to the symmetry group of the square?

Let $p$ be a prime. Find a formula for the number of conjugacy classes of elements of order $p$ in $S_n$.

If $S$ is all finitary permutations of $\Bbb N$ and $A$ is the alternating subgroup, prove $1\lhd A\lhd S$ is the only composition series of $S$

Irreducibility of exterior powers of representations of the symmetric group over finite fields

Is the symmetric group over 8 items, $S_8$, presented by $\langle x, y \mid x^2 = e, y^8 = e, (xy)^7 = e \rangle$?

Prove that $\tau \sigma \tau ^{-1}$ depends only on the lateral class of $\tau$ with respect to $Z(\sigma)$

Artin's Algebra: Homomorphism $S_4 \to S_3$

Find the conjugacy class in $S_n$ of $(12...n)$. What is the order of the centalizer of $(12...n)$ in $S_n$?

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