Question

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

score 376 · Answer 1 · 2019-05-10 05:04:23

376

Views

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

Published on 10 May 2019 - 5:04

score 358 · Answer 2 · 2019-05-12 12:27:15

358

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 12 May 2019 - 12:27

score 502 · Answer 3 · 2019-05-14 04:06:01

502

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 May 2019 - 4:06

score 150 · Answer 4 · 2026-03-25 04:39:10

150

Views

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

Published on 25 Mar 2026 - 4:39

score 84 · Answer 5 · 2019-05-30 08:34:24

84

Views

Semidirect product that is not isomorphic to direct product

Published on 30 May 2019 - 8:34

score 785 · Answer 6 · 2026-03-25 01:28:03

785

Views

Proof of associativity of semidirect product

Published on 25 Mar 2026 - 1:28

score 66 · Answer 7 · 2026-03-25 07:43:52

66

Views

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

Published on 25 Mar 2026 - 7:43

score 96 · Answer 8 · 2019-06-26 10:48:45

96

Views

Understanding mapping of vertices in Cayley graphs of semidirect products

Published on 26 Jun 2019 - 10:48

score 234 · Answer 9 · 2019-07-07 23:04:10

234

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 07 Jul 2019 - 23:04

score 225 · Answer 10 · 2019-07-07 23:55:16

225

Views

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

Published on 07 Jul 2019 - 23:55

score 98 · Answer 11 · 2019-07-25 07:45:42

98

Views

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

Published on 25 Jul 2019 - 7:45

score 174 · Answer 12 · 2019-07-25 10:06:27

174

Views

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

Published on 25 Jul 2019 - 10:06

score 50 · Answer 13 · 2019-07-28 20:14:26

50

Views

Is this an isomorphism for $D_8$?

Published on 28 Jul 2019 - 20:14

score 66 · Answer 14 · 2019-07-31 05:58:17

66

Views

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

Published on 31 Jul 2019 - 5:58

score 519 · Answer 15 · 2019-08-15 01:21:57

519

Views

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

Published on 15 Aug 2019 - 1:21

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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