Question

Given 2 elements $x,y \in S_4$, is there any particular trick to determining the subgroup generated by them?

score 97 · Answer 1 · 2026-03-27 22:55:14

97

Views

Given 2 elements $x,y \in S_4$, is there any particular trick to determining the subgroup generated by them?

Published on 27 Mar 2026 - 22:55

score 67 · Answer 2 · 2021-10-08 08:12:51

67

Views

Prove $\operatorname{ sgn}(\sigma)=\frac{D(X_{\sigma(1)},\cdots,X_{\sigma(n)})}{D(X_1,\cdots,X_n)}$

Published on 08 Oct 2021 - 8:12

score 59 · Answer 3 · 2026-03-27 22:52:54

59

Views

Cycle Index tables and a way to obtain $Z_m(S_p)$?

Published on 27 Mar 2026 - 22:52

score 83 · Answer 4 · 2021-10-09 12:48:11

83

Views

Is there a way to determine if an even permutation $a$ exists such that $a\tau a^{-1}=\sigma$

Published on 09 Oct 2021 - 12:48

score 28 · Answer 5 · 2021-10-09 18:40:20

28

Views

How to formalize notion of "up to ordering"

Published on 09 Oct 2021 - 18:40

score 334 · Answer 6 · 2021-10-10 16:16:22

334

Views

Prove that we have an isomorphism from the group generated by $1/x$, $(x-1)/x$ to the symmetric group $S_3$

Published on 10 Oct 2021 - 16:16

score 62 · Answer 7 · 2026-03-28 17:05:22

62

Views

Show that $A$ is a simple group.

Published on 28 Mar 2026 - 17:05

score 98 · Answer 8 · 2021-10-11 16:54:33

98

Views

Conjugation of Gal$(f)$, considered as a subgroup of $S_n$

Published on 11 Oct 2021 - 16:54

score 86 · Answer 9 · 2021-10-11 20:23:30

86

Views

Transitive action of $S_n$

Published on 11 Oct 2021 - 20:23

score 428 · Answer 10 · 2026-03-28 00:30:59

428

Views

How do I show $A_4$ is the only subgroup of order 12 of $S_4$ ? (Do not use Lagrange, index, cosets, normal subgroups, quotient groups)

Published on 28 Mar 2026 - 0:30

score 101 · Answer 11 · 2026-03-28 00:35:30

101

Views

centralizer of permutations in Symmetric group

Published on 28 Mar 2026 - 0:35

score 41 · Answer 12 · 2026-04-04 07:55:18

41

Views

Let A be an abelian group, m a positive integer and $f_{m}:A{\rightarrow}A$ be defined by $f_{m}(a)=ma$. Show that $f_{m}$ is a group homomorphism.

Published on 04 Apr 2026 - 7:55

score 153 · Answer 13 · 2026-02-23 08:08:32

153

Views

When is an integer power of a $12$-cycle a $12$-cycle?

Published on 23 Feb 2026 - 8:08

score 269 · Answer 14 · 2021-10-17 19:14:00

269

Views

Find all left cosets of $\langle(12), (34)\rangle$ in $S_4.$

Published on 17 Oct 2021 - 19:14

score 380 · Answer 15 · 2021-10-19 09:25:20

380

Views

Proof verification: Symmetric groups are group. What is a permutation group?

Published on 19 Oct 2021 - 9:25

List Question

Given 2 elements $x,y \in S_4$, is there any particular trick to determining the subgroup generated by them?

Prove $\operatorname{ sgn}(\sigma)=\frac{D(X_{\sigma(1)},\cdots,X_{\sigma(n)})}{D(X_1,\cdots,X_n)}$

Cycle Index tables and a way to obtain $Z_m(S_p)$?

Is there a way to determine if an even permutation $a$ exists such that $a\tau a^{-1}=\sigma$

How to formalize notion of "up to ordering"

Prove that we have an isomorphism from the group generated by $1/x$, $(x-1)/x$ to the symmetric group $S_3$

Show that $A$ is a simple group.

Conjugation of Gal$(f)$, considered as a subgroup of $S_n$

Transitive action of $S_n$

How do I show $A_4$ is the only subgroup of order 12 of $S_4$ ? (Do not use Lagrange, index, cosets, normal subgroups, quotient groups)

centralizer of permutations in Symmetric group

Let A be an abelian group, m a positive integer and $f_{m}:A{\rightarrow}A$ be defined by $f_{m}(a)=ma$. Show that $f_{m}$ is a group homomorphism.

When is an integer power of a $12$-cycle a $12$-cycle?

Find all left cosets of $\langle(12), (34)\rangle$ in $S_4.$

Proof verification: Symmetric groups are group. What is a permutation group?

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