Question

Basis transformation matrix for direct product space

score 166 · Answer 1 · 2026-04-13 02:18:55

166

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Basis transformation matrix for direct product space

Published on 13 Apr 2026 - 2:18

score 55 · Answer 2 · 2026-04-15 21:17:28

55

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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 15 Apr 2026 - 21:17

score 663 · Answer 3 · 2026-05-10 12:14:28

663

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Subgroups of $G\times H$

Published on 10 May 2026 - 12:14

score 64 · Answer 4 · 2026-04-15 15:49:36

64

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Showing some element is a zero divisor

Published on 15 Apr 2026 - 15:49

score 225 · Answer 5 · 2026-04-13 19:58:57

225

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About Sylow subgroup and internal direct product.

Published on 13 Apr 2026 - 19:58

score 1.1k · Answer 6 · 2026-04-16 01:18:36

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 16 Apr 2026 - 1:18

score 40 · Answer 7 · 2026-04-09 16:24:55

40

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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 09 Apr 2026 - 16:24

score 36 · Answer 8 · 2026-04-16 14:50:28

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 158 · Answer 9 · 2026-04-12 04:48:19

158

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Is the following cyclic group test wrong in WolframAlpha?

Published on 12 Apr 2026 - 4:48

score 36 · Answer 10 · 2026-04-15 18:19:46

36

Views

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

Published on 15 Apr 2026 - 18:19

score 250 · Answer 11 · 2026-04-13 14:55:20

250

Views

Classification of indecomposable abelian groups and direct product

Published on 13 Apr 2026 - 14:55

score 32 · Answer 12 · 2026-04-09 11:15:56

32

Views

Direct Product cancellation in Hopfian rings

Published on 09 Apr 2026 - 11:15

score 502 · Answer 13 · 2026-04-14 09:37:06

502

Views

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

Published on 14 Apr 2026 - 9:37

score 396 · Answer 14 · 2026-04-11 20:55:45

396

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

Published on 11 Apr 2026 - 20:55

score 363 · Answer 15 · 2026-04-11 11:33:54

363

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What are some applications of subdirect product?

Published on 11 Apr 2026 - 11:33

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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