Question

For finite collection of groups, $G_{1},G_{2},\dots, G_{n}$, $\exists G$ such that $G_{i}$ is a homomorphic image of $G$

score 46 · Answer 1 · 2016-11-14 12:40:15

46

Views

For finite collection of groups, $G_{1},G_{2},\dots, G_{n}$, $\exists G$ such that $G_{i}$ is a homomorphic image of $G$

Published on 14 Nov 2016 - 12:40

score 103 · Answer 2 · 2016-11-14 13:33:54

103

Views

$\forall m,n \geq 2$, $\exists$ non-cyclic group of order $n^{m}$

Published on 14 Nov 2016 - 13:33

score 680 · Answer 3 · 2016-11-16 10:22:22

680

Views

Intersection of elements of a internal direct product is the identity

Published on 16 Nov 2016 - 10:22

score 355 · Answer 4 · 2016-11-17 00:26:10

355

Views

Finding elements of a particular order in the direct product of abelian groups

Published on 17 Nov 2016 - 0:26

score 53 · Answer 5 · 2016-11-17 22:29:52

53

Views

characterizations of decomposable groups via normal complements and generalizations?

Published on 17 Nov 2016 - 22:29

score 476 · Answer 6 · 2016-11-27 03:41:21

476

Views

Showing $\Bbb Z_2 + \Bbb Z_3$ is isomorphic to $\Bbb Z_6$.

Published on 27 Nov 2016 - 3:41

score 278 · Answer 7 · 2016-11-28 01:45:51

278

Views

Smallest $n$ for non-isomorphic groups for external product of groups

Published on 28 Nov 2016 - 1:45

score 1.3k · Answer 8 · 2026-03-26 11:18:18

1.3k

Views

Why is the group of symmetries of a rectangular prism isomorphic to $D_4 \oplus Z_2$?

Published on 26 Mar 2026 - 11:18

score 198 · Answer 9 · 2026-03-26 11:01:23

198

Views

What are the free and torsion parts of $\mathbb{Z}\times\mathbb{Z}$, $\mathbb{Z}\times\mathbb{Z}_6$, and $\mathbb{Q}/\mathbb{Z}$?

Published on 26 Mar 2026 - 11:01

score 156 · Answer 10 · 2016-12-17 13:07:35

156

Views

Given that $G$ is subdirect product of $A$ and $B,$ and $G/G'$ is not subdirect product of $A/A'$ and $ B/B',$ this group contains $G'$?

Published on 17 Dec 2016 - 13:07

score 1.3k · Answer 11 · 2016-12-27 08:40:04

1.3k

Views

Can you get a basis for an infinite direct product of vector spaces from a basis for each factor?

Published on 27 Dec 2016 - 8:40

score 234 · Answer 12 · 2017-01-09 20:49:55

234

Views

Direct Decomposition of Groups

Published on 09 Jan 2017 - 20:49

score 78 · Answer 13 · 2017-01-24 10:46:49

78

Views

Centerless CR-radical: A Result Independent of the Axiom of Choice.

Published on 24 Jan 2017 - 10:46

score 94 · Answer 14 · 2017-02-12 17:32:48

94

Views

If $|G|=pqr$ show that $G\cong P\times QR$ where $P,Q,R$ are sylow-$p,q,r$ subgroups respectively under certain conditions

Published on 12 Feb 2017 - 17:32

score 61 · Answer 15 · 2026-03-25 12:55:31

61

Views

How to denote isomorphism/ ring direct product

Published on 25 Mar 2026 - 12:55

List Question

For finite collection of groups, $G_{1},G_{2},\dots, G_{n}$, $\exists G$ such that $G_{i}$ is a homomorphic image of $G$

$\forall m,n \geq 2$, $\exists$ non-cyclic group of order $n^{m}$

Intersection of elements of a internal direct product is the identity

Finding elements of a particular order in the direct product of abelian groups

characterizations of decomposable groups via normal complements and generalizations?

Showing $\Bbb Z_2 + \Bbb Z_3$ is isomorphic to $\Bbb Z_6$.

Smallest $n$ for non-isomorphic groups for external product of groups

Why is the group of symmetries of a rectangular prism isomorphic to $D_4 \oplus Z_2$?

What are the free and torsion parts of $\mathbb{Z}\times\mathbb{Z}$, $\mathbb{Z}\times\mathbb{Z}_6$, and $\mathbb{Q}/\mathbb{Z}$?

Given that $G$ is subdirect product of $A$ and $B,$ and $G/G'$ is not subdirect product of $A/A'$ and $ B/B',$ this group contains $G'$?

Can you get a basis for an infinite direct product of vector spaces from a basis for each factor?

Direct Decomposition of Groups

Centerless CR-radical: A Result Independent of the Axiom of Choice.

If $|G|=pqr$ show that $G\cong P\times QR$ where $P,Q,R$ are sylow-$p,q,r$ subgroups respectively under certain conditions

How to denote isomorphism/ ring direct product

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