Question

Computing all semidirect products $\mathbb{Z}/3\mathbb{Z}\rtimes D_8.$

score 86 · Answer 1 · 2026-03-29 16:28:00

86

Views

Computing all semidirect products $\mathbb{Z}/3\mathbb{Z}\rtimes D_8.$

Published on 29 Mar 2026 - 16:28

score 130 · Answer 2 · 2026-03-26 14:20:47

130

Views

$G$ is an extension of $\mathbb{Z}^2$ by $\mathbb{Z}$

Published on 26 Mar 2026 - 14:20

score 85 · Answer 3 · 2026-03-29 22:28:35

85

Views

Subgroups of semidirect product and commuting automorphism

Published on 29 Mar 2026 - 22:28

score 43 · Answer 4 · 2022-10-06 16:58:58

43

Views

Condition for a group G to be the product of subgroups

Published on 06 Oct 2022 - 16:58

score 57 · Answer 5 · 2026-03-21 04:15:23

57

Views

Unitary irreps of a semi-direct product

Published on 21 Mar 2026 - 4:15

score 92 · Answer 6 · 2022-10-14 03:52:13

92

Views

cardinality of a semi-direct product

Published on 14 Oct 2022 - 3:52

score 148 · Answer 7 · 2022-10-14 06:09:46

148

Views

Is semi-direct product uniquely defined?

Published on 14 Oct 2022 - 6:09

score 105 · Answer 8 · 2022-10-16 09:38:07

105

Views

Semidirect product and matrix groups

Published on 16 Oct 2022 - 9:38

score 148 · Answer 9 · 2022-10-20 15:52:47

148

Views

Classifying groups of order 8 (semidirect products)

Published on 20 Oct 2022 - 15:52

score 61 · Answer 10 · 2022-11-02 09:21:55

61

Views

Prove that if $G=L\rtimes_\theta H_1=L\rtimes_\theta H_2$ (inner semidirect products) then $H_1 \cong H_2$

Published on 02 Nov 2022 - 9:21

score 48 · Answer 11 · 2022-11-07 16:05:44

48

Views

$\mathbb{Z}_{p^2} \rtimes \mathbb{Z}_p $ is non abelian of order $p^3$ with element of order $p^2$

Published on 07 Nov 2022 - 16:05

score 130 · Answer 12 · 2022-11-18 03:42:26

130

Views

If $p<q$, $p\nmid q-1$, then “every group of order $pq$ is cyclic” iff “there is no nontrivial homomorphism from $ℤ_p$ into $\mathrm{Aut}(ℤ_q)$”.

Published on 18 Nov 2022 - 3:42

score 69 · Answer 13 · 2022-11-18 06:06:02

69

Views

If $|P|=p$, $|Q|=q$, $p, q$ primes, $p<q$ and $p|q-1$, then $Q\rtimes_{\varphi}P$ is nonabelian for nontrivial homomorphisms $\varphi: P\to Aut(Q)$.

Published on 18 Nov 2022 - 6:06

score 62 · Answer 14 · 2022-11-21 14:08:10

62

Views

example for $K\rtimes H\cong G\rtimes H$ and $K\ncong G$

Published on 21 Nov 2022 - 14:08

score 148 · Answer 15 · 2022-11-25 17:00:07

148

Views

$G$ noncyclic, $|G|=p^3$, $p$ an odd prime. Let $\varphi: x\mapsto x^p$. Show that if $|\text{ker}(\varphi)|=p^2$, then $E\cong Z_p\times Z_p$.

Published on 25 Nov 2022 - 17:00

List Question

Computing all semidirect products $\mathbb{Z}/3\mathbb{Z}\rtimes D_8.$

$G$ is an extension of $\mathbb{Z}^2$ by $\mathbb{Z}$

Subgroups of semidirect product and commuting automorphism

Condition for a group G to be the product of subgroups

Unitary irreps of a semi-direct product

cardinality of a semi-direct product

Is semi-direct product uniquely defined?

Semidirect product and matrix groups

Classifying groups of order 8 (semidirect products)

Prove that if $G=L\rtimes_\theta H_1=L\rtimes_\theta H_2$ (inner semidirect products) then $H_1 \cong H_2$

$\mathbb{Z}_{p^2} \rtimes \mathbb{Z}_p $ is non abelian of order $p^3$ with element of order $p^2$

If $p<q$, $p\nmid q-1$, then “every group of order $pq$ is cyclic” iff “there is no nontrivial homomorphism from $ℤ_p$ into $\mathrm{Aut}(ℤ_q)$”.

If $|P|=p$, $|Q|=q$, $p, q$ primes, $p<q$ and $p|q-1$, then $Q\rtimes_{\varphi}P$ is nonabelian for nontrivial homomorphisms $\varphi: P\to Aut(Q)$.

example for $K\rtimes H\cong G\rtimes H$ and $K\ncong G$

$G$ noncyclic, $|G|=p^3$, $p$ an odd prime. Let $\varphi: x\mapsto x^p$. Show that if $|\text{ker}(\varphi)|=p^2$, then $E\cong Z_p\times Z_p$.

Trending Questions

Popular # Hahtags

Popular Questions