Question

$H \unlhd G$, $\pi:G \to H$ is a group homomorphism with $\pi(h)=h$. Show that $G \cong H × G/H$

score 598 · Answer 1 · 2022-05-09 04:50:45

598

Views

$H \unlhd G$, $\pi:G \to H$ is a group homomorphism with $\pi(h)=h$. Show that $G \cong H × G/H$

Published on 09 May 2022 - 4:50

score 71 · Answer 2 · 2022-05-09 12:48:41

71

Views

Is the following statement in group theory true?

Published on 09 May 2022 - 12:48

score 321 · Answer 3 · 2022-05-11 12:51:27

321

Views

Prove that $G\cong H\times K$ if and only if there are homomorphisms...

Published on 11 May 2022 - 12:51

score 78 · Answer 4 · 2022-05-20 05:41:09

78

Views

Solution check request for the question: If $G=AB$ and $A\cap B=N,$ prove that $G/N\cong A/N\times B/N\\$

Published on 20 May 2022 - 5:41

score 83 · Answer 5 · 2022-05-21 23:27:42

83

Views

Prove that the direct product of $2$ subgroups is a subgroup

Published on 21 May 2022 - 23:27

score 46 · Answer 6 · 2022-05-21 23:32:09

46

Views

Construct subgroup of $\mathbb{Z_2} \times \mathbb{Z_2}$ where both groups involved in the direct product are not subgroups of $\mathbb{Z_2}$

Published on 21 May 2022 - 23:32

score 535 · Answer 7 · 2022-05-24 15:17:34

535

Views

How is the Lie algebra of a direct product of matrix Lie groups related to a direct sum?

Published on 24 May 2022 - 15:17

score 161 · Answer 8 · 2022-05-25 04:34:46

161

Views

Tensor product, direct product, and direct sum?

Published on 25 May 2022 - 4:34

score 49 · Answer 9 · 2022-06-01 12:18:53

49

Views

Show that $Z(G)=\prod\limits_{i=1}^n Z(N_i)$

Published on 01 Jun 2022 - 12:18

score 50 · Answer 10 · 2026-02-23 11:21:03

50

Views

Socle of a Hamiltonian group?

Published on 23 Feb 2026 - 11:21

score 60 · Answer 11 · 2022-07-04 11:39:26

60

Views

Find all the subgroups of $\mathbb{Z}_6\times \mathbb{Z}_6$ containing the diagonal $\{(a, a) \mid a\in\mathbb{Z}_6\}$.

Published on 04 Jul 2022 - 11:39

score 59 · Answer 12 · 2022-07-07 16:10:48

59

Views

How could I visualize the plane $\{(x_1,y_1,x_2,y_2)\in\mathbb{R}^4: x_1=y_1-1,x_2=y_2-1\}?$

Published on 07 Jul 2022 - 16:10

score 77 · Answer 13 · 2022-07-10 14:30:27

77

Views

For two subgroups $H, N$ of a non-abelian group $G$, if $HN\cong H\rtimes_{\tt A} N$, can we deduct $H\cap N=1$ if we know $N \unlhd HN$?

Published on 10 Jul 2022 - 14:30

score 62 · Answer 14 · 2022-07-10 17:14:04

62

Views

A question about the definition of semidirect product of groups

Published on 10 Jul 2022 - 17:14

score 145 · Answer 15 · 2022-07-17 13:31:55

145

Views

How to find subgroups of a product group containing the diagonal?

Published on 17 Jul 2022 - 13:31

List Question

$H \unlhd G$, $\pi:G \to H$ is a group homomorphism with $\pi(h)=h$. Show that $G \cong H × G/H$

Is the following statement in group theory true?

Prove that $G\cong H\times K$ if and only if there are homomorphisms...

Solution check request for the question: If $G=AB$ and $A\cap B=N,$ prove that $G/N\cong A/N\times B/N\\$

Prove that the direct product of $2$ subgroups is a subgroup

Construct subgroup of $\mathbb{Z_2} \times \mathbb{Z_2}$ where both groups involved in the direct product are not subgroups of $\mathbb{Z_2}$

How is the Lie algebra of a direct product of matrix Lie groups related to a direct sum?

Tensor product, direct product, and direct sum?

Show that $Z(G)=\prod\limits_{i=1}^n Z(N_i)$

Socle of a Hamiltonian group?

Find all the subgroups of $\mathbb{Z}_6\times \mathbb{Z}_6$ containing the diagonal $\{(a, a) \mid a\in\mathbb{Z}_6\}$.

How could I visualize the plane $\{(x_1,y_1,x_2,y_2)\in\mathbb{R}^4: x_1=y_1-1,x_2=y_2-1\}?$

For two subgroups $H, N$ of a non-abelian group $G$, if $HN\cong H\rtimes_{\tt A} N$, can we deduct $H\cap N=1$ if we know $N \unlhd HN$?

A question about the definition of semidirect product of groups

How to find subgroups of a product group containing the diagonal?

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