Question

Basis transformation matrix for direct product space

score 163 · Answer 1 · 2018-11-04 08:29:08

163

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Basis transformation matrix for direct product space

Published on 04 Nov 2018 - 8:29

score 52 · Answer 2 · 2018-11-05 01:05:35

52

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for any integer $n\ge2$, consider the group ${\bf Z}_{p^n}\oplus{\bf Z}_p$. Determine the number of cyclic subgroups of order $p$

Published on 05 Nov 2018 - 1:05

score 658 · Answer 3 · 2018-11-07 00:01:42

658

Views

Subgroups of $G\times H$

Published on 07 Nov 2018 - 0:01

score 61 · Answer 4 · 2026-03-25 02:58:59

61

Views

Showing some element is a zero divisor

Published on 25 Mar 2026 - 2:58

score 223 · Answer 5 · 2026-03-25 11:12:04

223

Views

About Sylow subgroup and internal direct product.

Published on 25 Mar 2026 - 11:12

score 1.1k · Answer 6 · 2018-11-21 02:12:54

1.1k

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In the category $\mathbf{Set}$ is "the product of an empty set of sets a one-element set"?

Published on 21 Nov 2018 - 2:12

score 37 · Answer 7 · 2018-11-21 04:30:27

37

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$\{\prod_{i=1}^{r} H_{i}\} \bigcap H_{r+1} = \{e\} \Rightarrow H_{i}\bigcap H_{j} = \{e\} \; \forall i\neq j$?

Published on 21 Nov 2018 - 4:30

score 33 · Answer 8 · 2018-11-21 04:51:24

Let $G=H_{1} \times H_{2} \dots \times H_{n}$ if and only if $ \; \forall g \in G$, $g= h_{1}h_{2}\ldots h_n$ where $h_{i} \in H_{i}$ is unique.

score 155 · Answer 9 · 2018-11-22 00:48:19

155

Views

Is the following cyclic group test wrong in WolframAlpha?

Published on 22 Nov 2018 - 0:48

score 33 · Answer 10 · 2018-12-08 10:35:33

33

Views

Group of order greater than 8 doesn't decompose into a direct product and Sylow 2-subgroup isomorphic quaternion group

Published on 08 Dec 2018 - 10:35

score 247 · Answer 11 · 2018-12-08 19:41:26

247

Views

Classification of indecomposable abelian groups and direct product

Published on 08 Dec 2018 - 19:41

score 29 · Answer 12 · 2018-12-10 07:49:30

29

Views

Direct Product cancellation in Hopfian rings

Published on 10 Dec 2018 - 7:49

score 499 · Answer 13 · 2018-12-22 06:18:00

499

Views

What does $O_p(G)$ mean in the context of a Fitting subgroup of $G$?

Published on 22 Dec 2018 - 6:18

score 393 · Answer 14 · 2019-01-04 17:23:20

393

Views

Construct a non trivial homomorphism from $\mathbb{Z}_2\times\mathbb{Z}_4$ to $\mathbb{Z}_8$

Published on 04 Jan 2019 - 17:23

score 360 · Answer 15 · 2026-03-25 14:06:25

360

Views

What are some applications of subdirect product?

Published on 25 Mar 2026 - 14:06

List Question

Basis transformation matrix for direct product space

for any integer $n\ge2$, consider the group ${\bf Z}_{p^n}\oplus{\bf Z}_p$. Determine the number of cyclic subgroups of order $p$

Subgroups of $G\times H$

Showing some element is a zero divisor

About Sylow subgroup and internal direct product.

In the category $\mathbf{Set}$ is "the product of an empty set of sets a one-element set"?

$\{\prod_{i=1}^{r} H_{i}\} \bigcap H_{r+1} = \{e\} \Rightarrow H_{i}\bigcap H_{j} = \{e\} \; \forall i\neq j$?

Let $G=H_{1} \times H_{2} \dots \times H_{n}$ if and only if $ \; \forall g \in G$, $g= h_{1}h_{2}\ldots h_n$ where $h_{i} \in H_{i}$ is unique.

Is the following cyclic group test wrong in WolframAlpha?

Group of order greater than 8 doesn't decompose into a direct product and Sylow 2-subgroup isomorphic quaternion group

Classification of indecomposable abelian groups and direct product

Direct Product cancellation in Hopfian rings

What does $O_p(G)$ mean in the context of a Fitting subgroup of $G$?

Construct a non trivial homomorphism from $\mathbb{Z}_2\times\mathbb{Z}_4$ to $\mathbb{Z}_8$

What are some applications of subdirect product?

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