List questions from semidirect-product

Published on 30 Mar 2026 - 3:53

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Does every virtually cyclic group $G$ have the form $G=H\ltimes N$?

Published on 04 Aug 2022 - 11:32

131

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Does a finite-by-(infinite dihedral) group have the form $N\rtimes H$ for a finite normal subgroup $N$ and a cyclic subgroup $H$?

Published on 28 Mar 2026 - 9:33

264

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Determine the group structure from its character table: a group of order $24$ as an example

Published on 30 Mar 2026 - 15:34

166

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Finite extensions of finitely generated free groups.

Published on 30 Mar 2026 - 8:31

145

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Is there a way to define other homorphisms, different from the conjugation mapping, in the definition of outer semidirect-products?

Published on 11 Aug 2022 - 16:26

87

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Are metacyclic $p$-groups semidirect products?

Published on 28 Mar 2026 - 16:21

55

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Let $H$ be an infinite hyperbolic group. Can $H \rtimes \mathbb Z$ ever be hyperbolic?

Published on 17 Aug 2022 - 18:06

47

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$3$-length of $(C_3\times C_3):GL(2,3)$ in GAP

Published on 30 Mar 2026 - 5:29

95

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The number of retracts of $G\ltimes \mathbb{Z}$

Published on 23 Feb 2026 - 18:47

123

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Let $G$ be a group, $\lambda:G\to S_G$ s.t. $\lambda(g)(x)=gx$, ${\rm Hol}(G)=\lambda(G){\rm Aut}(G)$. Prove ${\rm Hol}(G)=G\rtimes{\rm Aut}(G)$.

Published on 23 Feb 2026 - 0:28

105

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Conjugate actions and isomorphic semidirect products

Published on 02 Sep 2022 - 17:03

205

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Automorphism of $\mathbb{Z}^2\rtimes\mathbb{Z}$

Published on 29 Mar 2026 - 22:28

52

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Presentation of metacyclic groups $C_n \rtimes_s C_m$ with ${\rm ord}_n(s) < m$

Published on 30 Mar 2026 - 6:50

122

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Inverse limit of semidirect products

Published on 26 Mar 2026 - 23:11

List Question

Semidirect products in GAP - unexpected error

Does every virtually cyclic group $G$ have the form $G=H\ltimes N$?

Does a finite-by-(infinite dihedral) group have the form $N\rtimes H$ for a finite normal subgroup $N$ and a cyclic subgroup $H$?

Determine the group structure from its character table: a group of order $24$ as an example

Finite extensions of finitely generated free groups.

Is there a way to define other homorphisms, different from the conjugation mapping, in the definition of outer semidirect-products?

Are metacyclic $p$-groups semidirect products?

Let $H$ be an infinite hyperbolic group. Can $H \rtimes \mathbb Z$ ever be hyperbolic?

$3$-length of $(C_3\times C_3):GL(2,3)$ in GAP

The number of retracts of $G\ltimes \mathbb{Z}$

Let $G$ be a group, $\lambda:G\to S_G$ s.t. $\lambda(g)(x)=gx$, ${\rm Hol}(G)=\lambda(G){\rm Aut}(G)$. Prove ${\rm Hol}(G)=G\rtimes{\rm Aut}(G)$.

Conjugate actions and isomorphic semidirect products

Automorphism of $\mathbb{Z}^2\rtimes\mathbb{Z}$

Presentation of metacyclic groups $C_n \rtimes_s C_m$ with ${\rm ord}_n(s) < m$

Inverse limit of semidirect products

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