Question

Let $P$ be a Sylow $5$-subgroup of the symmetric group $S_{25}$ on $25$ letters. Show that there are two elements of $P$ that generate $P$ as a group.

score 143 · Answer 1 · 2019-06-18 03:09:04

143

Views

Let $P$ be a Sylow $5$-subgroup of the symmetric group $S_{25}$ on $25$ letters. Show that there are two elements of $P$ that generate $P$ as a group.

Published on 18 Jun 2019 - 3:09

score 763 · Answer 2 · 2019-06-20 02:22:47

763

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If $\tau=(1\ 2)(3\ 4)(5\ 6)(7\ 8)(9\ 10)$ determine whether there is an $n$-cycle $\sigma$ $(n\ge 10)$ s.t. $\sigma^k = \tau$

Published on 20 Jun 2019 - 2:22

score 55 · Answer 3 · 2026-03-25 14:22:29

55

Views

What subgroup of $S_4$ is this?

Published on 25 Mar 2026 - 14:22

score 56 · Answer 4 · 2019-06-23 07:19:19

56

Views

The number of transpositions in a representation of a permutation is even for even permutation and odd for odd permutation

Published on 23 Jun 2019 - 7:19

score 109 · Answer 5 · 2026-03-25 06:06:34

109

Views

Permutation of index and permutation of vector of powers of monomial

Published on 25 Mar 2026 - 6:06

score 146 · Answer 6 · 2026-03-26 16:05:16

146

Views

Algorithmically List Representatives of Conjugacy Classes of Symmetric Group

Published on 26 Mar 2026 - 16:05

score 97 · Answer 7 · 2019-06-30 22:22:30

97

Views

What are the possible values for n if there is an injective homomorphism from $Z_{n}$ to $S_{7}$

Published on 30 Jun 2019 - 22:22

score 580 · Answer 8 · 2019-07-02 07:21:21

580

Views

How many subgroups of $S_8$ with index $2$?

Published on 02 Jul 2019 - 7:21

score 148 · Answer 9 · 2019-07-02 16:29:17

148

Views

Find the order of permutation groups

Published on 02 Jul 2019 - 16:29

score 539 · Answer 10 · 2026-03-25 23:38:01

539

Views

Does $A_{17}$ have a subgroup of index $3$?

Published on 25 Mar 2026 - 23:38

score 97 · Answer 11 · 2026-03-25 23:14:20

97

Views

Organise "all possible voting schemes"

Published on 25 Mar 2026 - 23:14

score 271 · Answer 12 · 2026-03-25 14:25:26

271

Views

How is the standard representation of $S_n$ the direct sum of trivial representation and permutation representation?

Published on 25 Mar 2026 - 14:25

score 276 · Answer 13 · 2026-03-26 01:23:33

276

Views

If $H$ is a normal subgroup of $S_n$ where $(12)(34)∈ H$, $Sn/H \cong {e}$ or $Sn/H \cong Z/2Z$.

Published on 26 Mar 2026 - 1:23

score 57 · Answer 14 · 2019-07-12 05:56:16

57

Views

how to prove that all the homomorphisms from $~G\to K~$ are from specific form

Published on 12 Jul 2019 - 5:56

score 270 · Answer 15 · 2026-03-25 06:10:57

270

Views

GAP: how to obtain the Young Symmetrizer?

Published on 25 Mar 2026 - 6:10

List Question

Let $P$ be a Sylow $5$-subgroup of the symmetric group $S_{25}$ on $25$ letters. Show that there are two elements of $P$ that generate $P$ as a group.

If $\tau=(1\ 2)(3\ 4)(5\ 6)(7\ 8)(9\ 10)$ determine whether there is an $n$-cycle $\sigma$ $(n\ge 10)$ s.t. $\sigma^k = \tau$

What subgroup of $S_4$ is this?

The number of transpositions in a representation of a permutation is even for even permutation and odd for odd permutation

Permutation of index and permutation of vector of powers of monomial

Algorithmically List Representatives of Conjugacy Classes of Symmetric Group

What are the possible values for n if there is an injective homomorphism from $Z_{n}$ to $S_{7}$

How many subgroups of $S_8$ with index $2$?

Find the order of permutation groups

Does $A_{17}$ have a subgroup of index $3$?

Organise "all possible voting schemes"

How is the standard representation of $S_n$ the direct sum of trivial representation and permutation representation?

If $H$ is a normal subgroup of $S_n$ where $(12)(34)∈ H$, $Sn/H \cong {e}$ or $Sn/H \cong Z/2Z$.

how to prove that all the homomorphisms from $~G\to K~$ are from specific form

GAP: how to obtain the Young Symmetrizer?

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