Question

Can I get ${\rm{Inn}}(S_3)={\rm{Aut}}(S_3)$ from $\varphi\in{\rm{Aut}}(S_3)$ being equivalent to a faithful transitive action of $S_3$ on $\{1,2,3\}$?

score 192 · Answer 1 · 2026-03-31 15:14:33

192

Views

Can I get ${\rm{Inn}}(S_3)={\rm{Aut}}(S_3)$ from $\varphi\in{\rm{Aut}}(S_3)$ being equivalent to a faithful transitive action of $S_3$ on $\{1,2,3\}$?

Published on 31 Mar 2026 - 15:14

score 86 · Answer 2 · 2020-12-03 12:03:02

86

Views

A bijection for counting commuting pairs in finite group

Published on 03 Dec 2020 - 12:03

score 380 · Answer 3 · 2026-04-04 07:00:39

380

Views

Hatcher 1.3.27: Clarification on left and right actions

Published on 04 Apr 2026 - 7:00

score 159 · Answer 4 · 2026-04-01 10:39:47

159

Views

Help with an algebraic geometry result

Published on 01 Apr 2026 - 10:39

score 247 · Answer 5 · 2026-04-01 03:09:25

247

Views

Example of G-invariant ideal

Published on 01 Apr 2026 - 3:09

score 51 · Answer 6 · 2026-03-27 12:01:47

51

Views

Is $\mathbb{C}[V]^G \subset \mathbb{C}[V]$ flat?

Published on 27 Mar 2026 - 12:01

score 35 · Answer 7 · 2020-12-12 06:37:47

35

Views

Show that the group $R^\times$ acts transitively on the set $\{s\in R| (s) = (r)\}$ for a fixed r.

Published on 12 Dec 2020 - 6:37

score 181 · Answer 8 · 2020-12-12 11:06:11

181

Views

Solution check: group action.

Published on 12 Dec 2020 - 11:06

score 312 · Answer 9 · 2020-12-12 14:27:52

312

Views

Definition of group action.

Published on 12 Dec 2020 - 14:27

score 212 · Answer 10 · 2020-12-13 12:07:21

212

Views

Ambiguity in orbit space notation

Published on 13 Dec 2020 - 12:07

score 77 · Answer 11 · 2026-04-04 06:41:04

77

Views

Constructing elements of $\mathbb{Z}_p[\Gamma_n]$ from $\mathbb{Z}_p[\operatorname{Gal}(\mathbb{Q}(\zeta_{p^{n+1}})/\mathbb{Q})]$

Published on 04 Apr 2026 - 6:41

score 101 · Answer 12 · 2026-03-29 11:06:55

101

Views

If there is a convergence action on the space $X = R^{n+1}\cup S^{n}$, is it true that X is a closed ball?

Published on 29 Mar 2026 - 11:06

score 72 · Answer 13 · 2026-04-06 22:41:52

72

Views

zero sets of fundamental vector fields

Published on 06 Apr 2026 - 22:41

score 88 · Answer 14 · 2020-12-15 13:07:23

88

Views

Actions on left and right cosets of a subgroup of prime index.

Published on 15 Dec 2020 - 13:07

score 2.9k · Answer 15 · 2020-12-15 18:06:12

2.9k

Views

Textbook recommendation on group theory for graduate.

Published on 15 Dec 2020 - 18:06

List Question

Can I get ${\rm{Inn}}(S_3)={\rm{Aut}}(S_3)$ from $\varphi\in{\rm{Aut}}(S_3)$ being equivalent to a faithful transitive action of $S_3$ on $\{1,2,3\}$?

A bijection for counting commuting pairs in finite group

Hatcher 1.3.27: Clarification on left and right actions

Help with an algebraic geometry result

Example of G-invariant ideal

Is $\mathbb{C}[V]^G \subset \mathbb{C}[V]$ flat?

Show that the group $R^\times$ acts transitively on the set $\{s\in R| (s) = (r)\}$ for a fixed r.

Solution check: group action.

Definition of group action.

Ambiguity in orbit space notation

Constructing elements of $\mathbb{Z}_p[\Gamma_n]$ from $\mathbb{Z}_p[\operatorname{Gal}(\mathbb{Q}(\zeta_{p^{n+1}})/\mathbb{Q})]$

If there is a convergence action on the space $X = R^{n+1}\cup S^{n}$, is it true that X is a closed ball?

zero sets of fundamental vector fields

Actions on left and right cosets of a subgroup of prime index.

Textbook recommendation on group theory for graduate.

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