Question

A finite group $G$ and fixed $k\geq 1$ where for every $n\geq 1$, the $n$-direct product $G^n=G\times\dots\times G$ is $k$-generated?

score 64 · Answer 1 · 2026-05-10 17:39:17

64

Views

A finite group $G$ and fixed $k\geq 1$ where for every $n\geq 1$, the $n$-direct product $G^n=G\times\dots\times G$ is $k$-generated?

Published on 10 May 2026 - 17:39

score 42 · Answer 2 · 2026-04-11 10:47:25

42

Views

Alternative definitions of "internal direct product"

Published on 11 Apr 2026 - 10:47

score 47 · Answer 3 · 2026-04-10 23:48:35

47

Views

What is a good way to prove that the function $\Bbb Z_n \rightarrow \Bbb Z_u \times\Bbb Z_v$ is well defined?

Published on 10 Apr 2026 - 23:48

score 1.5k · Answer 4 · 2026-04-13 14:49:33

1.5k

Views

Finding all composition series of $S_3 \times Z_2$

Published on 13 Apr 2026 - 14:49

score 833 · Answer 5 · 2026-04-16 14:37:23

833

Views

Is $D_n$ isomorphic to $C_n \times C_2$?

Published on 16 Apr 2026 - 14:37

score 430 · Answer 6 · 2026-04-13 17:04:13

430

Views

Is there a nice way to express the quotient of the direct product of a family of groups with the corresponding direct sum?

Published on 13 Apr 2026 - 17:04

score 312 · Answer 7 · 2026-04-15 11:26:07

312

Views

Product of all normal subgroups of a group

Published on 15 Apr 2026 - 11:26

score 1.4k · Answer 8 · 2026-04-12 23:52:07

1.4k

Views

Is there another name for Goursat's Lemma on subgroups of a direct product of groups?

Published on 12 Apr 2026 - 23:52

score 374 · Answer 9 · 2026-04-12 02:53:33

374

Views

When is the decomposition of a group element as a product of elements of two subgroups unique?

Published on 12 Apr 2026 - 2:53

score 275 · Answer 10 · 2026-04-15 15:41:35

275

Views

If $E_i$ is Banach space, is $\prod_iE_i$ a Banach space as well?

Published on 15 Apr 2026 - 15:41

score 762 · Answer 11 · 2026-04-17 09:39:21

762

Views

Number of elements of order 3 in $C_3 \times C_9$

Published on 17 Apr 2026 - 9:39

score 106 · Answer 12 · 2026-04-14 19:13:31

106

Views

On the direct product of abelian groups

Published on 14 Apr 2026 - 19:13

score 143 · Answer 13 · 2026-04-16 23:01:03

143

Views

Subgroup of the direct product of the rings or groups

Published on 16 Apr 2026 - 23:01

score 1.2k · Answer 14 · 2026-04-17 04:44:05

1.2k

Views

Showing that a finite abelian group is isomorphic to a subgroup of a direct product of cyclic groups, without the fundamental theorem

Published on 17 Apr 2026 - 4:44

score 221 · Answer 15 · 2026-05-10 18:43:49

221

Views

Understanding Direct product of subgroups in GAP

Published on 10 May 2026 - 18:43

List Question

A finite group $G$ and fixed $k\geq 1$ where for every $n\geq 1$, the $n$-direct product $G^n=G\times\dots\times G$ is $k$-generated?

Alternative definitions of "internal direct product"

What is a good way to prove that the function $\Bbb Z_n \rightarrow \Bbb Z_u \times\Bbb Z_v$ is well defined?

Finding all composition series of $S_3 \times Z_2$

Is $D_n$ isomorphic to $C_n \times C_2$?

Is there a nice way to express the quotient of the direct product of a family of groups with the corresponding direct sum?

Product of all normal subgroups of a group

Is there another name for Goursat's Lemma on subgroups of a direct product of groups?

When is the decomposition of a group element as a product of elements of two subgroups unique?

If $E_i$ is Banach space, is $\prod_iE_i$ a Banach space as well?

Number of elements of order 3 in $C_3 \times C_9$

On the direct product of abelian groups

Subgroup of the direct product of the rings or groups

Showing that a finite abelian group is isomorphic to a subgroup of a direct product of cyclic groups, without the fundamental theorem

Understanding Direct product of subgroups in GAP

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