Question

Semi-direct product $C_p : C_3$

score 123 · Answer 1 · 2026-03-29 15:59:54

123

Views

Semi-direct product $C_p : C_3$

Published on 29 Mar 2026 - 15:59

score 65 · Answer 2 · 2021-03-14 11:09:48

65

Views

Understanding groups of order 12 as it appears in Dummit.

Published on 14 Mar 2021 - 11:09

score 70 · Answer 3 · 2026-03-29 15:59:39

70

Views

Identify subgroup of a semidirect product in GAP

Published on 29 Mar 2026 - 15:59

score 110 · Answer 4 · 2021-03-27 19:18:40

110

Views

Is the (outer) semidirect product, $N \rtimes H$, ever characterized as a group of bijections on a group containing $N$?

Published on 27 Mar 2021 - 19:18

score 58 · Answer 5 · 2021-03-29 13:22:33

58

Views

Naming the groups in a semidirect product

Published on 29 Mar 2021 - 13:22

score 38 · Answer 6 · 2026-03-28 09:44:12

38

Views

Characterization of permutable subgroups (direct product)

Published on 28 Mar 2026 - 9:44

score 124 · Answer 7 · 2021-04-14 19:35:58

124

Views

$O(n)\cong SO(n)\rtimes O(1)$

Published on 14 Apr 2021 - 19:35

score 95 · Answer 8 · 2021-04-23 05:48:47

95

Views

Is Symmetric group on 5 symbols is the semi-direct product?

Published on 23 Apr 2021 - 5:48

score 250 · Answer 9 · 2026-03-29 23:46:20

250

Views

For $N\unlhd G$ for $\mathfrak{B}$-group $G$ with $G/N$ a free $\mathfrak{B}$-group, show $\exists H\le G$ with $G=HN$ and $H\cap N=1$

Published on 29 Mar 2026 - 23:46

score 32 · Answer 10 · 2021-04-27 15:52:18

32

Views

Show subgroups of semidirect product are closed

Published on 27 Apr 2021 - 15:52

score 55 · Answer 11 · 2021-05-05 06:25:17

55

Views

Can this group be written as a semidirect product?

Published on 05 May 2021 - 6:25

score 39 · Answer 12 · 2021-05-05 08:52:28

39

Views

Let $(n,h)\in G = N \rtimes H$. Is it true that $\mathrm{ord}(n,h)=\mathrm{lcm}(\mathrm{ord}(n),\mathrm{ord}(h))$?

Published on 05 May 2021 - 8:52

score 111 · Answer 13 · 2026-03-28 11:32:49

111

Views

How do I show a semidirect product of relatively-prime ordered groups is isomorphic to the direct product of those groups?

Published on 28 Mar 2026 - 11:32

score 173 · Answer 14 · 2026-03-28 11:27:21

173

Views

$\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups.

Published on 28 Mar 2026 - 11:27

score 45 · Answer 15 · 2021-05-30 21:52:39

45

Views

Is the nontrivial semidirect product of $C_3^2$ by $Q$ unique?

Published on 30 May 2021 - 21:52

List Question

Semi-direct product $C_p : C_3$

Understanding groups of order 12 as it appears in Dummit.

Identify subgroup of a semidirect product in GAP

Is the (outer) semidirect product, $N \rtimes H$, ever characterized as a group of bijections on a group containing $N$?

Naming the groups in a semidirect product

Characterization of permutable subgroups (direct product)

$O(n)\cong SO(n)\rtimes O(1)$

Is Symmetric group on 5 symbols is the semi-direct product?

For $N\unlhd G$ for $\mathfrak{B}$-group $G$ with $G/N$ a free $\mathfrak{B}$-group, show $\exists H\le G$ with $G=HN$ and $H\cap N=1$

Show subgroups of semidirect product are closed

Can this group be written as a semidirect product?

Let $(n,h)\in G = N \rtimes H$. Is it true that $\mathrm{ord}(n,h)=\mathrm{lcm}(\mathrm{ord}(n),\mathrm{ord}(h))$?

How do I show a semidirect product of relatively-prime ordered groups is isomorphic to the direct product of those groups?

$\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups.

Is the nontrivial semidirect product of $C_3^2$ by $Q$ unique?

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