Question

Class of nilpotency of semidirect product

score 86 · Answer 1 · 2023-03-12 18:32:45

86

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Class of nilpotency of semidirect product

Published on 12 Mar 2023 - 18:32

score 47 · Answer 2 · 2023-03-23 18:23:59

47

Views

Is the holomorph of generalized quaternion group embedded in the affine group of Galois ring?

Published on 23 Mar 2023 - 18:23

score 25 · Answer 3 · 2024-03-17 17:51:07

25

Views

The socle of the holomorph of the simple group $A_{5}$

Published on 17 Mar 2024 - 17:51

score 1.5k · Answer 4 · 2015-01-05 18:09:29

1.5k

Views

The holomorph of $Z_2 \times Z_2$

Published on 05 Jan 2015 - 18:09

score 328 · Answer 5 · 2016-05-09 21:35:15

328

Views

Holomorph of Cyclic $p$-groups

Published on 09 May 2016 - 21:35

score 263 · Answer 6 · 2012-05-28 05:46:41

263

Views

Why is the holomorph of a group $G$ a group of transformations of $G$?

Published on 28 May 2012 - 5:46

score 68 · Answer 7 · 2020-12-15 22:18:38

68

Views

Prove $\forall z\in H$, $\frac{|f'(z)|}{Im f(z)} ≤ \frac{1}{Im f(z)}$ given f holomorphic using Schwarz Lemma

Published on 15 Dec 2020 - 22:18

score 116 · Answer 8 · 2021-04-11 20:26:11

116

Views

Conjugation of regular subgroups in the holomorph

Published on 11 Apr 2021 - 20:26

score 154 · Answer 9 · 2021-06-09 01:38:21

154

Views

Is a holomorph of a group unique?

Published on 09 Jun 2021 - 1:38

score 36 · Answer 10 · 2021-07-04 20:07:16

36

Views

Cauchy Integralformula comprehension question

Published on 04 Jul 2021 - 20:07

score 656 · Answer 11 · 2022-01-07 20:05:53

656

Views

Showing ${\rm Aut}(Q_{2^n})\cong{\rm Hol}(\Bbb Z_{2^{n-1}})$ for $n>3$

Published on 07 Jan 2022 - 20:05

score 32 · Answer 12 · 2022-03-27 18:44:55

32

Views

In $\operatorname{Hol}(\Bbb{Z}_{10})$, is every mapping from $G\rightarrow\operatorname{Aut}(G)$ just an identity mapping?

Published on 27 Mar 2022 - 18:44

score 54 · Answer 13 · 2022-03-28 17:45:02

54

Views

Is $\operatorname{Hol}(D_4)$ isomorphic to a familiar group?

Published on 28 Mar 2022 - 17:45

score 28 · Answer 14 · 2022-04-27 04:43:02

28

Views

Holomorphic function over a real interval has an extension to a subset of the complex plane

Published on 27 Apr 2022 - 4:43

score 122 · Answer 15 · 2022-08-22 09:37:16

122

Views

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 22 Aug 2022 - 9:37

List Question

Class of nilpotency of semidirect product

Is the holomorph of generalized quaternion group embedded in the affine group of Galois ring?

The socle of the holomorph of the simple group $A_{5}$

The holomorph of $Z_2 \times Z_2$

Holomorph of Cyclic $p$-groups

Why is the holomorph of a group $G$ a group of transformations of $G$?

Prove $\forall z\in H$, $\frac{|f'(z)|}{Im f(z)} ≤ \frac{1}{Im f(z)}$ given f holomorphic using Schwarz Lemma

Conjugation of regular subgroups in the holomorph

Is a holomorph of a group unique?

Cauchy Integralformula comprehension question

Showing ${\rm Aut}(Q_{2^n})\cong{\rm Hol}(\Bbb Z_{2^{n-1}})$ for $n>3$

In $\operatorname{Hol}(\Bbb{Z}_{10})$, is every mapping from $G\rightarrow\operatorname{Aut}(G)$ just an identity mapping?

Is $\operatorname{Hol}(D_4)$ isomorphic to a familiar group?

Holomorphic function over a real interval has an extension to a subset of the complex plane

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 ${\rm Hol}(G)=G\rtimes{\rm Aut}(G)$.

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