Question

When are direct products cancellative for finite algebras?

score 61 · Answer 1 · 2021-10-27 15:55:31

61

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When are direct products cancellative for finite algebras?

Published on 27 Oct 2021 - 15:55

score 1.1k · Answer 2 · 2021-10-29 16:32:58

1.1k

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Suppose that $H$ and $K$ are normal subgroups of $G$ such that $H \cap K=\{e\}$. Show that $G$ is isomorphic with some subgroup of $G/H \times G/K$.

Published on 29 Oct 2021 - 16:32

score 204 · Answer 3 · 2021-11-03 03:35:35

204

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Constructing a field from a direct product of fields

Published on 03 Nov 2021 - 3:35

score 51 · Answer 4 · 2021-11-13 17:21:39

51

Views

Direct product of modules and the axiom of choice

Published on 13 Nov 2021 - 17:21

score 77 · Answer 5 · 2021-11-14 21:10:08

77

Views

How to prove $ \Phi:H_{1}\times...\times H_{n}\to G $ defined by $ \Phi\left(h_{1},...,h_{n}\right):=h_{1}\cdot...\cdot h_{n} $ is an isomorphism

Published on 14 Nov 2021 - 21:10

score 50 · Answer 6 · 2021-11-17 10:25:02

50

Views

Every abelian group of order $9p^2$ where $p\equiv 2\bmod 3$, can be written as the direct product of two cyclic subgroups.

Published on 17 Nov 2021 - 10:25

score 25 · Answer 7 · 2021-11-18 10:22:20

25

Views

Count the subgroups of order $25$ in $C_{75} \times C_{10}$

Published on 18 Nov 2021 - 10:22

score 1.5k · Answer 8 · 2021-11-19 11:27:23

1.5k

Views

How many subgroups does $\mathbb{Z}_{13}\times\mathbb{Z}_{13}$ have?

Published on 19 Nov 2021 - 11:27

score 204 · Answer 9 · 2021-11-22 23:43:27

204

Views

Is homotopy group of infinite product of spaces a direct sum or a direct product of groups?

Published on 22 Nov 2021 - 23:43

score 112 · Answer 10 · 2021-11-29 12:19:38

112

Views

Quotient of the direct product of cyclic groups

Published on 29 Nov 2021 - 12:19

score 125 · Answer 11 · 2021-12-03 19:14:26

125

Views

External direct product of a family of group homomorphisms

Published on 03 Dec 2021 - 19:14

score 84 · Answer 12 · 2026-03-27 11:46:54

84

Views

Discovering and describing the homomorphisms returned by the sagemath function direct_product()

Published on 27 Mar 2026 - 11:46

score 393 · Answer 13 · 2026-03-28 03:56:18

393

Views

Isomorphisms for Infinite Direct Products of Groups

Published on 28 Mar 2026 - 3:56

score 127 · Answer 14 · 2021-12-09 15:34:58

127

Views

Let $G$ be a group and let $H_1,H_2\unlhd G$ such that $H_1\cap H_2 = \{1\}$ and $H_1H_2=G.$ Prove $G\simeq H_1\times H_2$

Published on 09 Dec 2021 - 15:34

score 123 · Answer 15 · 2021-12-10 09:43:42

123

Views

Addition and Tensor product of Vector spaces for beginners : Concrete example

Published on 10 Dec 2021 - 9:43

List Question

When are direct products cancellative for finite algebras?

Suppose that $H$ and $K$ are normal subgroups of $G$ such that $H \cap K=\{e\}$. Show that $G$ is isomorphic with some subgroup of $G/H \times G/K$.

Constructing a field from a direct product of fields

Direct product of modules and the axiom of choice

How to prove $ \Phi:H_{1}\times...\times H_{n}\to G $ defined by $ \Phi\left(h_{1},...,h_{n}\right):=h_{1}\cdot...\cdot h_{n} $ is an isomorphism

Every abelian group of order $9p^2$ where $p\equiv 2\bmod 3$, can be written as the direct product of two cyclic subgroups.

Count the subgroups of order $25$ in $C_{75} \times C_{10}$

How many subgroups does $\mathbb{Z}_{13}\times\mathbb{Z}_{13}$ have?

Is homotopy group of infinite product of spaces a direct sum or a direct product of groups?

Quotient of the direct product of cyclic groups

External direct product of a family of group homomorphisms

Discovering and describing the homomorphisms returned by the sagemath function direct_product()

Isomorphisms for Infinite Direct Products of Groups

Let $G$ be a group and let $H_1,H_2\unlhd G$ such that $H_1\cap H_2 = \{1\}$ and $H_1H_2=G.$ Prove $G\simeq H_1\times H_2$

Addition and Tensor product of Vector spaces for beginners : Concrete example

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