List questions from direct-product

Published on 27 Mar 2026 - 22:57

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Classification of group extension.

Published on 14 Jan 2021 - 12:38

62

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Is there always exists a product over a semigroup?

Published on 07 Feb 2021 - 5:39

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Let $G$ and $H$ be abelian groups. Show that the product $G\times H$ is also abelian.

Published on 11 Feb 2021 - 20:15

73

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Show that exists an epimorphism $\phi_i: T \rightarrow G_i$ and find $\ker(\phi_i)$

Published on 12 Feb 2021 - 20:17

153

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Elements and Conjugacy Classes of a group

Published on 15 Feb 2021 - 15:39

157

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Write as the internal direct product of two proper subgroups in every possible way.

Published on 15 Feb 2021 - 16:05

26

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Understanding an example of a finitely generated projective module which is not free.

Published on 16 Feb 2021 - 6:09

62

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Direct product of Hilbert spaces

Published on 23 Feb 2021 - 15:51

567

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When is commutative reduced ring a finite direct product of domains?

Published on 23 Feb 2026 - 9:32

38

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Confusion about direct sums of $\mathbb{Z}/pq\mathbb{Z}$ where $p, q$ prime

Published on 05 Mar 2021 - 7:08

217

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Find all normal subgroups of $S_3 \times \mathbb{Z}_6$

Published on 12 Mar 2021 - 12:35

228

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If $G=G_1\times\dots\times G_n$ for abelian $G_i$, then ${\rm Aut}(G)$ is isomorphic to a specific general linear group.

Published on 12 Mar 2021 - 20:12

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Let $G=\Bbb Z\times\Bbb Z$ be additive and $H=\{0\}\times\Bbb Z$. Show that: a) $H\le G$. b) $H\cong \Bbb Z$.

Published on 21 Mar 2021 - 22:46

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Notation for ordered pairs of congruence classes

Published on 22 Mar 2021 - 2:20

List Question

Let $H, K \lhd G$, then $G = HK \iff G / (H \cap K) \cong G / H \times G / K$

Classification of group extension.

Is there always exists a product over a semigroup?

Let $G$ and $H$ be abelian groups. Show that the product $G\times H$ is also abelian.

Show that exists an epimorphism $\phi_i: T \rightarrow G_i$ and find $\ker(\phi_i)$

Elements and Conjugacy Classes of a group

Write as the internal direct product of two proper subgroups in every possible way.

Understanding an example of a finitely generated projective module which is not free.

Direct product of Hilbert spaces

When is commutative reduced ring a finite direct product of domains?

Confusion about direct sums of $\mathbb{Z}/pq\mathbb{Z}$ where $p, q$ prime

Find all normal subgroups of $S_3 \times \mathbb{Z}_6$

If $G=G_1\times\dots\times G_n$ for abelian $G_i$, then ${\rm Aut}(G)$ is isomorphic to a specific general linear group.

Let $G=\Bbb Z\times\Bbb Z$ be additive and $H=\{0\}\times\Bbb Z$. Show that: a) $H\le G$. b) $H\cong \Bbb Z$.

Notation for ordered pairs of congruence classes

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