Question

Proving a criterion for recognizing when a group $G$ is a direct product of 2 groups

score 184 · Answer 1 · 2026-03-28 01:24:06

184

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Proving a criterion for recognizing when a group $G$ is a direct product of 2 groups

Published on 28 Mar 2026 - 1:24

score 116 · Answer 2 · 2020-09-24 10:36:51

116

Views

Proving a criterion for recognizing when a group $G$ is a semidirect product of 2 groups

Published on 24 Sep 2020 - 10:36

score 151 · Answer 3 · 2026-03-28 01:15:29

151

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The importance of $G \cong K \times H$ is just to create the split short exact sequence.

Published on 28 Mar 2026 - 1:15

score 264 · Answer 4 · 2026-03-28 20:57:06

264

Views

Understanding how reflection acts on rotation in $D_{6}.$

Published on 28 Mar 2026 - 20:57

score 64 · Answer 5 · 2020-09-26 19:01:16

64

Views

Show that $S_{4} \cong V \rtimes_{\phi} S_{3}$

Published on 26 Sep 2020 - 19:01

score 42 · Answer 6 · 2020-09-28 13:01:11

42

Views

Let, $N,K,N',K'$ be groups and $N\cong N',K\cong K'$. Does $N\rtimes K\cong N'\rtimes K'$?

Published on 28 Sep 2020 - 13:01

score 31 · Answer 7 · 2020-10-03 05:37:35

31

Views

Need help understanding example of semidirect product (continued)

Published on 03 Oct 2020 - 5:37

score 44 · Answer 8 · 2020-10-16 11:02:25

44

Views

Understanding the semidirect product when expressed as a linear transformation and determining the minimal polynomial, eigenvalues

Published on 16 Oct 2020 - 11:02

score 82 · Answer 9 · 2020-10-21 03:21:57

82

Views

Isomorphisms between Semi Direct Products

Published on 21 Oct 2020 - 3:21

score 63 · Answer 10 · 2020-10-22 00:09:54

63

Views

Writing $\mathbb{Z}_{p^2}$ as central extension of $\mathbb{Z}_{p}$ by $\mathbb{Z}_{p}$

Published on 22 Oct 2020 - 0:09

score 70 · Answer 11 · 2026-03-28 03:02:21

70

Views

how did we know the action in $\mathbb{Z}_{11} \rtimes_{\varphi} \mathbb{Z}_{5}$?

Published on 28 Mar 2026 - 3:02

score 140 · Answer 12 · 2026-03-26 07:33:48

140

Views

Homomorphisms of a Semidirect Product

Published on 26 Mar 2026 - 7:33

score 289 · Answer 13 · 2020-10-26 06:07:38

289

Views

residually finite semidirect product

Published on 26 Oct 2020 - 6:07

score 62 · Answer 14 · 2026-03-29 09:10:05

62

Views

Alternative characterisation of group defined by nested semidirect products

Published on 29 Mar 2026 - 9:10

score 68 · Answer 15 · 2026-03-29 03:36:24

68

Views

If $N$ is a normal subgroup of semidirect product group of $N$ and $H$ where $H$ is generated by $a$ and $b$, is $ab=ba$?

Published on 29 Mar 2026 - 3:36

List Question

Proving a criterion for recognizing when a group $G$ is a direct product of 2 groups

Proving a criterion for recognizing when a group $G$ is a semidirect product of 2 groups

The importance of $G \cong K \times H$ is just to create the split short exact sequence.

Understanding how reflection acts on rotation in $D_{6}.$

Show that $S_{4} \cong V \rtimes_{\phi} S_{3}$

Let, $N,K,N',K'$ be groups and $N\cong N',K\cong K'$. Does $N\rtimes K\cong N'\rtimes K'$?

Need help understanding example of semidirect product (continued)

Understanding the semidirect product when expressed as a linear transformation and determining the minimal polynomial, eigenvalues

Isomorphisms between Semi Direct Products

Writing $\mathbb{Z}_{p^2}$ as central extension of $\mathbb{Z}_{p}$ by $\mathbb{Z}_{p}$

how did we know the action in $\mathbb{Z}_{11} \rtimes_{\varphi} \mathbb{Z}_{5}$?

Homomorphisms of a Semidirect Product

residually finite semidirect product

Alternative characterisation of group defined by nested semidirect products

If $N$ is a normal subgroup of semidirect product group of $N$ and $H$ where $H$ is generated by $a$ and $b$, is $ab=ba$?

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