Question

There does not exist a subgroup $H$ of $S_n$ with $|S_n:H|=n$ and $H$ does not fix any element of $\{1,\ldots,n\}$.

score 139 · Answer 1 · 2021-06-25 14:57:11

139

Views

There does not exist a subgroup $H$ of $S_n$ with $|S_n:H|=n$ and $H$ does not fix any element of $\{1,\ldots,n\}$.

Published on 25 Jun 2021 - 14:57

score 47 · Answer 2 · 2021-06-27 18:42:54

47

Views

Every coset of $V_4$ in $S_4$ contains exactly one element from the set

Published on 27 Jun 2021 - 18:42

score 380 · Answer 3 · 2026-04-04 03:19:15

380

Views

How is injectivity enough to show function is an isomorphism?

Published on 04 Apr 2026 - 3:19

score 95 · Answer 4 · 2021-07-01 20:10:25

95

Views

Asymptotics for the probability that two $n$-cycles generate $S_n$ (or $A_n$).

Published on 01 Jul 2021 - 20:10

score 218 · Answer 5 · 2026-03-29 06:28:53

218

Views

Isomorphism between $D_3$ and $S_3$

Published on 29 Mar 2026 - 6:28

score 256 · Answer 6 · 2026-03-28 21:26:49

256

Views

Why is $S_3 / A_3$ cyclic group of order $2$?

Published on 28 Mar 2026 - 21:26

score 164 · Answer 7 · 2026-03-28 02:03:14

164

Views

Can every countable locally-finite group be embedded into $S_\infty$?

Published on 28 Mar 2026 - 2:03

score 74 · Answer 8 · 2021-07-08 11:21:02

74

Views

Fixed points of elements of $S_n$

Published on 08 Jul 2021 - 11:21

score 110 · Answer 9 · 2026-04-01 12:49:53

110

Views

Subspace of 3D Rotation Group that Provides Unique Cube Orientations

Published on 01 Apr 2026 - 12:49

score 109 · Answer 10 · 2021-07-15 06:16:04

109

Views

Let $G = S_n$, fix $i \in \{1,...,n\}$ and let $G_i = \{\sigma \in G ~|~ \sigma(i) = i\}$ .Then find $|G_i|?$.

Published on 15 Jul 2021 - 6:16

score 173 · Answer 11 · 2021-07-15 18:08:44

173

Views

Representations of symmetric (and alternating) groups over finite fields.

Published on 15 Jul 2021 - 18:08

score 289 · Answer 12 · 2026-04-01 05:46:34

289

Views

How to find the automorphism group of the graph mentioned in the question?

Published on 01 Apr 2026 - 5:46

score 429 · Answer 13 · 2021-07-20 18:58:20

429

Views

Show that $S(X)$ is abelian if and only if $|X|\le 2$

Published on 20 Jul 2021 - 18:58

score 157 · Answer 14 · 2021-07-20 23:07:22

157

Views

Is the regular group action of $G$ on itself doubly transitive?

Published on 20 Jul 2021 - 23:07

score 96 · Answer 15 · 2026-03-28 21:34:21

96

Views

Description of $S_4/H$ as a set where $H$ is order $8$ subgroup of $S_4$

Published on 28 Mar 2026 - 21:34

List Question

There does not exist a subgroup $H$ of $S_n$ with $|S_n:H|=n$ and $H$ does not fix any element of $\{1,\ldots,n\}$.

Every coset of $V_4$ in $S_4$ contains exactly one element from the set

How is injectivity enough to show function is an isomorphism?

Asymptotics for the probability that two $n$-cycles generate $S_n$ (or $A_n$).

Isomorphism between $D_3$ and $S_3$

Why is $S_3 / A_3$ cyclic group of order $2$?

Can every countable locally-finite group be embedded into $S_\infty$?

Fixed points of elements of $S_n$

Subspace of 3D Rotation Group that Provides Unique Cube Orientations

Let $G = S_n$, fix $i \in \{1,...,n\}$ and let $G_i = \{\sigma \in G ~|~ \sigma(i) = i\}$ .Then find $|G_i|?$.

Representations of symmetric (and alternating) groups over finite fields.

How to find the automorphism group of the graph mentioned in the question?

Show that $S(X)$ is abelian if and only if $|X|\le 2$

Is the regular group action of $G$ on itself doubly transitive?

Description of $S_4/H$ as a set where $H$ is order $8$ subgroup of $S_4$

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