Question

Subgroups of index $p^2$ of $(\mathbb{Z}/p^2\mathbb{Z})^\times\ltimes \mathbb{Z}/p\mathbb{Z}$

score 44 · Answer 1 · 2020-03-26 21:01:16

44

Views

Subgroups of index $p^2$ of $(\mathbb{Z}/p^2\mathbb{Z})^\times\ltimes \mathbb{Z}/p\mathbb{Z}$

Published on 26 Mar 2020 - 21:01

score 224 · Answer 2 · 2026-03-25 06:12:20

224

Views

Wreath product, semi-direct product, and partitions

Published on 25 Mar 2026 - 6:12

score 90 · Answer 3 · 2020-04-10 11:09:54

90

Views

Clarification regarding condition of semidirect product of cyclic groups

Published on 10 Apr 2020 - 11:09

score 339 · Answer 4 · 2020-04-11 17:31:11

339

Views

Why is trivial intersection of groups $N$ and $H$ not required in the definition of outer semi-direct products?

Published on 11 Apr 2020 - 17:31

score 95 · Answer 5 · 2020-04-13 00:24:47

95

Views

Semidirect product of point stabiliser and regular normal subgroup.

Published on 13 Apr 2020 - 0:24

score 49 · Answer 6 · 2026-03-25 12:33:51

49

Views

Why can the homomorphism $\phi$ in semi-direct products only be varied by inner automorphisms upon changing the complement group?

Published on 25 Mar 2026 - 12:33

score 63 · Answer 7 · 2026-03-16 07:45:45

63

Views

Some clarifications required about the two extremes of general extensions (semi-direct products and central extensions)

Published on 16 Mar 2026 - 7:45

score 91 · Answer 8 · 2020-04-15 02:59:48

91

Views

Semidirect product and group action

Published on 15 Apr 2020 - 2:59

score 57 · Answer 9 · 2020-04-20 15:47:17

57

Views

When can we "multiply through" by the kernel of a homomorphism?

Published on 20 Apr 2020 - 15:47

score 123 · Answer 10 · 2026-03-25 12:30:36

123

Views

Is group extension unique?

Published on 25 Mar 2026 - 12:30

score 98 · Answer 11 · 2020-05-02 19:28:28

98

Views

Constructing $\mathrm{SL}(2,5)\rtimes\mathbb{Z}_{11}^2$ in GAP

Published on 02 May 2020 - 19:28

score 114 · Answer 12 · 2026-03-25 12:34:45

114

Views

Why does every $\varphi: K \to \mathrm{Out}(H)$ determine an unique extension of $H$ by $K$ when $Z(H) = 1$?

Published on 25 Mar 2026 - 12:34

score 65 · Answer 13 · 2020-05-04 17:24:53

65

Views

Determining the homomorphism $\varphi: H \to \mathrm{Aut}(K)$ given a section $s: H \to G$

Published on 04 May 2020 - 17:24

score 175 · Answer 14 · 2020-05-08 06:43:39

175

Views

Closed-form exponential and logarithmic map of Galilei group

Published on 08 May 2020 - 6:43

score 82 · Answer 15 · 2026-03-25 12:37:34

82

Views

$M<K\rtimes H$ is a semidirect product?

Published on 25 Mar 2026 - 12:37

List Question

Subgroups of index $p^2$ of $(\mathbb{Z}/p^2\mathbb{Z})^\times\ltimes \mathbb{Z}/p\mathbb{Z}$

Wreath product, semi-direct product, and partitions

Clarification regarding condition of semidirect product of cyclic groups

Why is trivial intersection of groups $N$ and $H$ not required in the definition of outer semi-direct products?

Semidirect product of point stabiliser and regular normal subgroup.

Why can the homomorphism $\phi$ in semi-direct products only be varied by inner automorphisms upon changing the complement group?

Some clarifications required about the two extremes of general extensions (semi-direct products and central extensions)

Semidirect product and group action

When can we "multiply through" by the kernel of a homomorphism?

Is group extension unique?

Constructing $\mathrm{SL}(2,5)\rtimes\mathbb{Z}_{11}^2$ in GAP

Why does every $\varphi: K \to \mathrm{Out}(H)$ determine an unique extension of $H$ by $K$ when $Z(H) = 1$?

Determining the homomorphism $\varphi: H \to \mathrm{Aut}(K)$ given a section $s: H \to G$

Closed-form exponential and logarithmic map of Galilei group

$M<K\rtimes H$ is a semidirect product?

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