Question

Is $N \trianglelefteq G$?

score 106 · Answer 1 · 2022-07-29 03:22:54

106

Views

Is $N \trianglelefteq G$?

Published on 29 Jul 2022 - 3:22

score 109 · Answer 2 · 2022-07-29 12:25:28

109

Views

If all subgroups of direct product are direct products, then orders are coprime

Published on 29 Jul 2022 - 12:25

score 153 · Answer 3 · 2026-03-28 09:34:23

153

Views

Index of the direct product of subgroups

Published on 28 Mar 2026 - 9:34

score 391 · Answer 4 · 2022-08-31 17:03:15

391

Views

Prove that the group generated by sum of two subgroups is isomorphic with their cartesian product

Published on 31 Aug 2022 - 17:03

score 146 · Answer 5 · 2022-09-02 10:58:21

146

Views

Number of subgroups of order $4$ in the direct product $S_2\times S_4$.

Published on 02 Sep 2022 - 10:58

score 204 · Answer 6 · 2022-09-09 18:59:08

204

Views

Let $H,K\le G$, abelian $G$, and let $\phi:G\to H$ be a hom. s.t. 1) $\phi(h)=h\forall h\in H$, 2) $\text{Ker }\phi=K$. Show $G=H\oplus K$

Published on 09 Sep 2022 - 18:59

score 48 · Answer 7 · 2022-09-10 12:02:56

48

Views

All possible normal subgroups of a direct product.

Published on 10 Sep 2022 - 12:02

score 299 · Answer 8 · 2022-09-10 17:51:04

299

Views

How to finish the proof of: If $N\unlhd G=H\times K$, then $N$ is abelian or $N$ intersects $H \times \{e\}$ or $\{e\} \times K$ non trivially

Published on 10 Sep 2022 - 17:51

score 68 · Answer 9 · 2022-10-09 02:03:29

68

Views

Calculating the direct product and the cross product

Published on 09 Oct 2022 - 2:03

score 101 · Answer 10 · 2022-10-13 17:26:44

101

Views

Neccesary and sufficient condition for a direct product of proper subgroups to be isomorphic to the whole group

Published on 13 Oct 2022 - 17:26

score 58 · Answer 11 · 2026-02-23 20:40:56

58

Views

Prove or give counter example: $G \cong N \times G/N \Rightarrow N$ has a normal complement.

Published on 23 Feb 2026 - 20:40

score 77 · Answer 12 · 2022-10-19 19:29:41

77

Views

Confusion about direct limit of vector spaces

Published on 19 Oct 2022 - 19:29

score 135 · Answer 13 · 2022-10-28 03:52:51

135

Views

If $H,K$ are finite groups with $\text{gcd}(|H|,|K|)=1$, then $\text{Aut}(H \times K) \cong \text{Aut}(H) \times \text{Aut}(K)$.

Published on 28 Oct 2022 - 3:52

score 43 · Answer 14 · 2022-11-02 01:35:44

43

Views

Has this 'group product equivalence quotient' construction been substantially studied?

Published on 02 Nov 2022 - 1:35

score 159 · Answer 15 · 2022-11-06 11:45:16

159

Views

Confusion about the direct sum of abelian/nonabelian groups

Published on 06 Nov 2022 - 11:45

List Question

Is $N \trianglelefteq G$?

If all subgroups of direct product are direct products, then orders are coprime

Index of the direct product of subgroups

Prove that the group generated by sum of two subgroups is isomorphic with their cartesian product

Number of subgroups of order $4$ in the direct product $S_2\times S_4$.

Let $H,K\le G$, abelian $G$, and let $\phi:G\to H$ be a hom. s.t. 1) $\phi(h)=h\forall h\in H$, 2) $\text{Ker }\phi=K$. Show $G=H\oplus K$

All possible normal subgroups of a direct product.

How to finish the proof of: If $N\unlhd G=H\times K$, then $N$ is abelian or $N$ intersects $H \times \{e\}$ or $\{e\} \times K$ non trivially

Calculating the direct product and the cross product

Neccesary and sufficient condition for a direct product of proper subgroups to be isomorphic to the whole group

Prove or give counter example: $G \cong N \times G/N \Rightarrow N$ has a normal complement.

Confusion about direct limit of vector spaces

If $H,K$ are finite groups with $\text{gcd}(|H|,|K|)=1$, then $\text{Aut}(H \times K) \cong \text{Aut}(H) \times \text{Aut}(K)$.

Has this 'group product equivalence quotient' construction been substantially studied?

Confusion about the direct sum of abelian/nonabelian groups

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