Question

Why isn't $1 \to \mathbb{Z}_2 \to \mathbb{Z}_4 \to \mathbb{Z}_2 \to 1$ a split extension?

score 129 · Answer 1 · 2026-03-26 03:12:38

129

Views

Why isn't $1 \to \mathbb{Z}_2 \to \mathbb{Z}_4 \to \mathbb{Z}_2 \to 1$ a split extension?

Published on 26 Mar 2026 - 3:12

score 7.5k · Answer 2 · 2016-03-19 15:02:42

7.5k

Views

Intuition about the semidirect product of groups

Published on 19 Mar 2016 - 15:02

score 39 · Answer 3 · 2026-03-28 22:31:12

39

Views

If $G$ is cyclic of order $2$ show $|H^1(G,\mathbb{Z})|=2$.

Published on 28 Mar 2026 - 22:31

score 309 · Answer 4 · 2016-03-22 19:49:17

309

Views

Find a non-trivial outer automorphism of $A_n$?

Published on 22 Mar 2016 - 19:49

score 381 · Answer 5 · 2016-03-23 18:51:19

381

Views

Do homomorphisms $H \to \operatorname{Aut}(K)$ that coincide at the level of $\operatorname{Out}(K)$ induce isomorphic semidirect products?

Published on 23 Mar 2016 - 18:51

score 289 · Answer 6 · 2016-03-26 00:15:45

289

Views

Homomorphisms $H \to \operatorname{Aut}(K)$ that induce isomorphic semidirect products for centerless $K$

Published on 26 Mar 2016 - 0:15

score 686 · Answer 7 · 2016-04-04 04:54:13

686

Views

Is this intuition for the semidirect product of groups correct?

Published on 04 Apr 2016 - 4:54

score 36 · Answer 8 · 2016-04-07 09:04:11

36

Views

Is it true that if $bk\in Z(B\rtimes K)$ then $b\in Z(B)$?

Published on 07 Apr 2016 - 9:04

score 161 · Answer 9 · 2016-04-08 19:47:10

161

Views

Understanding a group of order $2^{25}.97^2$

Published on 08 Apr 2016 - 19:47

score 660 · Answer 10 · 2016-04-13 10:42:05

660

Views

Center of a semidirect product

Published on 13 Apr 2016 - 10:42

score 421 · Answer 11 · 2016-04-14 00:22:48

421

Views

Subgroups of the Semi-Direct Product $\mathbb{Z}/7\mathbb{Z} \rtimes (\mathbb{Z}/7\mathbb{Z})^{\times}$

Published on 14 Apr 2016 - 0:22

score 2.3k · Answer 12 · 2026-03-27 13:47:28

2.3k

Views

Direct Product and Semi-direct Product between $S_{3}$ and $Z_{2}$, and Related Problem

Published on 27 Mar 2026 - 13:47

score 152 · Answer 13 · 2016-05-20 18:42:04

152

Views

subgroup of a semidirect product

Published on 20 May 2016 - 18:42

score 98 · Answer 14 · 2016-05-21 14:27:45

98

Views

problem about inner semidirect product

Published on 21 May 2016 - 14:27

score 288 · Answer 15 · 2026-03-27 15:16:53

288

Views

External Semidirect product and isomorphism

Published on 27 Mar 2026 - 15:16

List Question

Why isn't $1 \to \mathbb{Z}_2 \to \mathbb{Z}_4 \to \mathbb{Z}_2 \to 1$ a split extension?

Intuition about the semidirect product of groups

If $G$ is cyclic of order $2$ show $|H^1(G,\mathbb{Z})|=2$.

Find a non-trivial outer automorphism of $A_n$?

Do homomorphisms $H \to \operatorname{Aut}(K)$ that coincide at the level of $\operatorname{Out}(K)$ induce isomorphic semidirect products?

Homomorphisms $H \to \operatorname{Aut}(K)$ that induce isomorphic semidirect products for centerless $K$

Is this intuition for the semidirect product of groups correct?

Is it true that if $bk\in Z(B\rtimes K)$ then $b\in Z(B)$?

Understanding a group of order $2^{25}.97^2$

Center of a semidirect product

Subgroups of the Semi-Direct Product $\mathbb{Z}/7\mathbb{Z} \rtimes (\mathbb{Z}/7\mathbb{Z})^{\times}$

Direct Product and Semi-direct Product between $S_{3}$ and $Z_{2}$, and Related Problem

subgroup of a semidirect product

problem about inner semidirect product

External Semidirect product and isomorphism

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