Question

Show that $G=S_3S_5\rtimes S_2$ where $|G|=30$ and $S_p$ is a $p$-Sylow subgroup

score 46 · Answer 1 · 2021-10-08 03:27:13

46

Views

Show that $G=S_3S_5\rtimes S_2$ where $|G|=30$ and $S_p$ is a $p$-Sylow subgroup

Published on 08 Oct 2021 - 3:27

score 111 · Answer 2 · 2021-10-14 20:13:58

111

Views

Which groups are a non-trivial semidirect product of abelian groups?

Published on 14 Oct 2021 - 20:13

score 55 · Answer 3 · 2021-10-17 21:09:52

55

Views

If $H \unlhd G$ then is $H \unlhd G \rtimes K$

Published on 17 Oct 2021 - 21:09

score 804 · Answer 4 · 2026-03-26 12:33:51

804

Views

Understanding the definition of group split extensions

Published on 26 Mar 2026 - 12:33

score 149 · Answer 5 · 2021-11-01 16:06:48

149

Views

If a short exact sequence splits we have a semidirect product

Published on 01 Nov 2021 - 16:06

score 74 · Answer 6 · 2026-03-30 00:04:13

74

Views

Show that $G= \langle x,y\mid x^2,xyx^{-1}y=e \rangle$ is a semidirect product of two of its subgroups

Published on 30 Mar 2026 - 0:04

score 98 · Answer 7 · 2026-03-26 06:29:07

98

Views

Show $G=\langle\delta\rangle\ltimes D$ is nilpotent of class $2$.

Published on 26 Mar 2026 - 6:29

score 293 · Answer 8 · 2021-12-07 05:06:37

293

Views

Group of order $pq$

Published on 07 Dec 2021 - 5:06

score 66 · Answer 9 · 2021-12-12 12:29:12

66

Views

Obtaining splitting of quotient map from semi-direct product

Published on 12 Dec 2021 - 12:29

score 63 · Answer 10 · 2021-12-13 15:54:36

63

Views

Find all semidirect products $\mathbb{Z}_{8} \rtimes \mathbb{Z}_{4}$ up to isomorphism

Published on 13 Dec 2021 - 15:54

score 42 · Answer 11 · 2026-03-26 12:36:31

42

Views

Showing the existence of an automorphism between two semidirect products

Published on 26 Mar 2026 - 12:36

score 43 · Answer 12 · 2026-03-26 04:30:36

43

Views

A question about equivariance to 3D transformations using semi-direct and direct products.

Published on 26 Mar 2026 - 4:30

score 103 · Answer 13 · 2021-12-20 20:26:46

103

Views

Showing, for $G=\langle\delta\rangle\ltimes(A\times A)$ and abelian $A$, that $Z(G)=G'\cong A$.

Published on 20 Dec 2021 - 20:26

score 198 · Answer 14 · 2021-12-26 14:53:01

198

Views

Characterization of the isomorphic semidirect products

Published on 26 Dec 2021 - 14:53

score 90 · Answer 15 · 2022-01-01 20:12:37

90

Views

Prove this isomorphism about semidirect product $((\oplus_1^k \mathbb{Z}/2) \oplus \mathbb{Z}/n) \rtimes_{\varphi} \mathbb{Z}/2$.

Published on 01 Jan 2022 - 20:12

List Question

Show that $G=S_3S_5\rtimes S_2$ where $|G|=30$ and $S_p$ is a $p$-Sylow subgroup

Which groups are a non-trivial semidirect product of abelian groups?

If $H \unlhd G$ then is $H \unlhd G \rtimes K$

Understanding the definition of group split extensions

If a short exact sequence splits we have a semidirect product

Show that $G= \langle x,y\mid x^2,xyx^{-1}y=e \rangle$ is a semidirect product of two of its subgroups

Show $G=\langle\delta\rangle\ltimes D$ is nilpotent of class $2$.

Group of order $pq$

Obtaining splitting of quotient map from semi-direct product

Find all semidirect products $\mathbb{Z}_{8} \rtimes \mathbb{Z}_{4}$ up to isomorphism

Showing the existence of an automorphism between two semidirect products

A question about equivariance to 3D transformations using semi-direct and direct products.

Showing, for $G=\langle\delta\rangle\ltimes(A\times A)$ and abelian $A$, that $Z(G)=G'\cong A$.

Characterization of the isomorphic semidirect products

Prove this isomorphism about semidirect product $((\oplus_1^k \mathbb{Z}/2) \oplus \mathbb{Z}/n) \rtimes_{\varphi} \mathbb{Z}/2$.

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