Question

Find all semidirect products of $(\mathbb{Z}_4,+)$ by $C_2 $

score 379 · Answer 1 · 2026-04-15 08:17:47

379

Views

Find all semidirect products of $(\mathbb{Z}_4,+)$ by $C_2 $

Published on 15 Apr 2026 - 8:17

score 361 · Answer 2 · 2026-04-16 07:00:09

361

Views

Find all group of order $20$ which is a semidirect product of a cyclic group of order $4$ by a cyclic group of order $5$

Published on 16 Apr 2026 - 7:00

score 505 · Answer 3 · 2026-04-14 20:48:57

505

Views

$N\rtimes_{\phi}H\cong N\rtimes_{\phi\circ\psi}H$ for $N,H$ be groups, $\phi \colon H\rightarrow Aut(N)$ be a homomorphism, $\psi \in Aut(H)$

Published on 14 Apr 2026 - 20:48

score 151 · Answer 4 · 2026-05-10 15:45:53

151

Views

Abelianization of $\mathbb{Z}\ltimes_\varphi \mathbb{Z}^n$

Published on 10 May 2026 - 15:45

score 87 · Answer 5 · 2026-04-10 18:19:52

87

Views

Semidirect product that is not isomorphic to direct product

Published on 10 Apr 2026 - 18:19

score 788 · Answer 6 · 2026-05-10 20:17:15

788

Views

Proof of associativity of semidirect product

Published on 10 May 2026 - 20:17

score 69 · Answer 7 · 2026-05-10 15:51:40

69

Views

Question regarding writing a group of order $p^2qr$ using notations

Published on 10 May 2026 - 15:51

score 100 · Answer 8 · 2026-05-10 17:01:13

100

Views

Understanding mapping of vertices in Cayley graphs of semidirect products

Published on 10 May 2026 - 17:01

score 238 · Answer 9 · 2026-05-10 18:48:26

238

Views

For all $n > 0$ express $D_{2n}$ as a semidirect product $\mathbb Z_n \rtimes_\theta \mathbb Z_2$, finding $\theta$ explicitly.

Published on 10 May 2026 - 18:48

score 228 · Answer 10 · 2026-04-16 14:10:39

228

Views

On subgroup structure of the p-group $G\simeq (Z/pZ)^{m}\rtimes(Z/pZ)$

Published on 16 Apr 2026 - 14:10

score 102 · Answer 11 · 2026-05-10 18:44:51

102

Views

How to obtain the product of elements in a semidirect product using GAP

Published on 10 May 2026 - 18:44

score 177 · Answer 12 · 2026-04-13 04:57:14

177

Views

Identifying the kernel of induced homorphism with the kernel of group action of G on the left cosets of H

Published on 13 Apr 2026 - 4:57

score 54 · Answer 13 · 2026-05-11 01:18:19

54

Views

Is this an isomorphism for $D_8$?

Published on 11 May 2026 - 1:18

score 69 · Answer 14 · 2026-05-10 16:59:46

69

Views

Computing the multiplication of elements to generate the Cayley graph of a semidirect product

Published on 10 May 2026 - 16:59

score 522 · Answer 15 · 2026-04-14 18:53:29

522

Views

If $q$ is not a divisor of $p-1$, then $G$ is cyclic. An open discussion on different proofs.

Published on 14 Apr 2026 - 18:53

List Question

Find all semidirect products of $(\mathbb{Z}_4,+)$ by $C_2 $

Find all group of order $20$ which is a semidirect product of a cyclic group of order $4$ by a cyclic group of order $5$

$N\rtimes_{\phi}H\cong N\rtimes_{\phi\circ\psi}H$ for $N,H$ be groups, $\phi \colon H\rightarrow Aut(N)$ be a homomorphism, $\psi \in Aut(H)$

Abelianization of $\mathbb{Z}\ltimes_\varphi \mathbb{Z}^n$

Semidirect product that is not isomorphic to direct product

Proof of associativity of semidirect product

Question regarding writing a group of order $p^2qr$ using notations

Understanding mapping of vertices in Cayley graphs of semidirect products

For all $n > 0$ express $D_{2n}$ as a semidirect product $\mathbb Z_n \rtimes_\theta \mathbb Z_2$, finding $\theta$ explicitly.

On subgroup structure of the p-group $G\simeq (Z/pZ)^{m}\rtimes(Z/pZ)$

How to obtain the product of elements in a semidirect product using GAP

Identifying the kernel of induced homorphism with the kernel of group action of G on the left cosets of H

Is this an isomorphism for $D_8$?

Computing the multiplication of elements to generate the Cayley graph of a semidirect product

If $q$ is not a divisor of $p-1$, then $G$ is cyclic. An open discussion on different proofs.

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