Question

A question on the Klein-4 group and permutations.

score 114 · Answer 1 · 2020-09-11 17:10:54

114

Views

A question on the Klein-4 group and permutations.

Published on 11 Sep 2020 - 17:10

score 174 · Answer 2 · 2026-03-31 06:00:28

174

Views

Describe a finite group as an automorphism group

Published on 31 Mar 2026 - 6:00

score 388 · Answer 3 · 2020-09-14 05:47:29

388

Views

Prove that there doesn't exist any normal subgroup $H$ such that $S_5/H $ is isomorphic to $S_4$

Published on 14 Sep 2020 - 5:47

score 151 · Answer 4 · 2020-09-14 07:09:18

151

Views

Is there a normal subgroup $H$ such that $S_6/H$ is isomorphic to $S_5$

Published on 14 Sep 2020 - 7:09

score 84 · Answer 5 · 2026-03-29 03:35:32

84

Views

What is the asymptotic of finite group Cayley length?

Published on 29 Mar 2026 - 3:35

score 158 · Answer 6 · 2020-09-14 15:47:57

158

Views

Prove by group actions that there doesn't exist any normal subgroup $H$ such that $S_5/H $ is isomorphic to $S_4$

Published on 14 Sep 2020 - 15:47

score 70 · Answer 7 · 2026-04-03 00:21:16

70

Views

Show that if $\frac {k!} {2} \lt n,$ then $G$ has a non-trivial proper normal subgroup.

Published on 03 Apr 2026 - 0:21

score 135 · Answer 8 · 2020-09-14 19:46:02

135

Views

Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?

Published on 14 Sep 2020 - 19:46

score 465 · Answer 9 · 2020-09-15 06:14:36

465

Views

Let $K=${$(12)(34),(13)(24),(14)(23),1$} .Prove that $K$ is a normal subgroup of $S_4$.

Published on 15 Sep 2020 - 6:14

score 38 · Answer 10 · 2026-03-27 05:41:40

38

Views

Solving cycles - Permutation group

Published on 27 Mar 2026 - 5:41

score 116 · Answer 11 · 2026-04-03 00:22:53

116

Views

Prove/disprove: $p>3$ prime. There doesn't exist any $H\lhd S_p$, $|H|=p$, such that $S_p/H\cong S_{p-1}$.

Published on 03 Apr 2026 - 0:22

score 637 · Answer 12 · 2020-09-17 02:08:43

637

Views

Show that $V_{\lambda'} \cong V_\lambda \otimes U$ where $V_\lambda$ is the Specht module and $U$ is the sign representation of $S_n$.

Published on 17 Sep 2020 - 2:08

score 79 · Answer 13 · 2020-09-17 08:19:39

79

Views

Is there any mathematical formula or method to compute the values of Landau function (by hand)?

Published on 17 Sep 2020 - 8:19

score 135 · Answer 14 · 2020-09-17 20:54:53

135

Views

Isomorphism $\phi:S_n\rightarrow S_A$.

Published on 17 Sep 2020 - 20:54

score 228 · Answer 15 · 2020-09-18 13:25:36

228

Views

Prove that $(1\ 2\ 3)$ cannot be a cube of any element in the symmetric group $S_n.$

Published on 18 Sep 2020 - 13:25

List Question

A question on the Klein-4 group and permutations.

Describe a finite group as an automorphism group

Prove that there doesn't exist any normal subgroup $H$ such that $S_5/H $ is isomorphic to $S_4$

Is there a normal subgroup $H$ such that $S_6/H$ is isomorphic to $S_5$

What is the asymptotic of finite group Cayley length?

Prove by group actions that there doesn't exist any normal subgroup $H$ such that $S_5/H $ is isomorphic to $S_4$

Show that if $\frac {k!} {2} \lt n,$ then $G$ has a non-trivial proper normal subgroup.

Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?

Let $K=${$(12)(34),(13)(24),(14)(23),1$} .Prove that $K$ is a normal subgroup of $S_4$.

Solving cycles - Permutation group

Prove/disprove: $p>3$ prime. There doesn't exist any $H\lhd S_p$, $|H|=p$, such that $S_p/H\cong S_{p-1}$.

Show that $V_{\lambda'} \cong V_\lambda \otimes U$ where $V_\lambda$ is the Specht module and $U$ is the sign representation of $S_n$.

Is there any mathematical formula or method to compute the values of Landau function (by hand)?

Isomorphism $\phi:S_n\rightarrow S_A$.

Prove that $(1\ 2\ 3)$ cannot be a cube of any element in the symmetric group $S_n.$

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