Question

Is every direct product of (finite) cyclic groups abelian?

score 701 · Answer 1 · 2021-01-11 18:08:04

701

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Is every direct product of (finite) cyclic groups abelian?

Published on 11 Jan 2021 - 18:08

score 37 · Answer 2 · 2021-01-15 08:40:12

37

Views

Embedding finite $p$-groups in principal congruence subgroup

Published on 15 Jan 2021 - 8:40

score 141 · Answer 3 · 2026-03-26 22:55:34

141

Views

How to choose ultraproducts to prove that the class of finite ($p$, torsion) groups is not elementary?

Published on 26 Mar 2026 - 22:55

score 79 · Answer 4 · 2026-03-26 03:11:09

79

Views

How to show that $G$ is nilpotent based on these conditions

Published on 26 Mar 2026 - 3:11

score 114 · Answer 5 · 2021-02-03 21:54:48

114

Views

Show an example of a finite abelian $p$-group that has $p^2 + p + 1$ subgroups of order $p$

Published on 03 Feb 2021 - 21:54

score 54 · Answer 6 · 2021-02-07 04:17:40

54

Views

Why $\Psi(H) \le \exp(G)$ for any subgroup $H$ of a finite $p$-group $G$ where $\Psi(H)=\frac{\Sigma_{h\in H}|h|}{|H|}$?

Published on 07 Feb 2021 - 4:17

score 533 · Answer 7 · 2026-03-25 19:05:12

533

Views

The number of groups of order 32

Published on 25 Mar 2026 - 19:05

score 128 · Answer 8 · 2026-03-27 23:32:01

128

Views

Show that a group of order $2^2 \cdot 5 \cdot 23^r$ is solvable but not simple.

Published on 27 Mar 2026 - 23:32

score 74 · Answer 9 · 2021-02-17 02:47:22

74

Views

"The p-power bounding" right multiplication in a finite group G under some special conditions

Published on 17 Feb 2021 - 2:47

score 56 · Answer 10 · 2021-03-02 12:45:01

56

Views

If $p$ is a prime then all the non trivial subgroups of $G$ with $\lvert G\rvert=p^2$ are cyclic

Published on 02 Mar 2021 - 12:45

score 44 · Answer 11 · 2021-03-08 22:17:26

44

Views

In a group $G$, of order $p^k$ has a subgroup of order $p^{k-1}$ prove this subgroup is normal.

Published on 08 Mar 2021 - 22:17

score 35 · Answer 12 · 2021-04-05 02:23:16

35

Views

Reference for "Every finite $p$-group can be expressed as a section of a powerful $p$-group"

Published on 05 Apr 2021 - 2:23

score 262 · Answer 13 · 2026-03-25 22:26:10

262

Views

Is there any function in GAP finding all maximal elementary abelian subgroup of a $p$-group $P$?

Published on 25 Mar 2026 - 22:26

score 106 · Answer 14 · 2026-03-25 09:26:20

106

Views

Frattini subgroup of p-groups characteristics

Published on 25 Mar 2026 - 9:26

score 873 · Answer 15 · 2026-03-25 23:51:43

873

Views

How to find minimal generating sets efficiently?

Published on 25 Mar 2026 - 23:51

List Question

Is every direct product of (finite) cyclic groups abelian?

Embedding finite $p$-groups in principal congruence subgroup

How to choose ultraproducts to prove that the class of finite ($p$, torsion) groups is not elementary?

How to show that $G$ is nilpotent based on these conditions

Show an example of a finite abelian $p$-group that has $p^2 + p + 1$ subgroups of order $p$

Why $\Psi(H) \le \exp(G)$ for any subgroup $H$ of a finite $p$-group $G$ where $\Psi(H)=\frac{\Sigma_{h\in H}|h|}{|H|}$?

The number of groups of order 32

Show that a group of order $2^2 \cdot 5 \cdot 23^r$ is solvable but not simple.

"The p-power bounding" right multiplication in a finite group G under some special conditions

If $p$ is a prime then all the non trivial subgroups of $G$ with $\lvert G\rvert=p^2$ are cyclic

In a group $G$, of order $p^k$ has a subgroup of order $p^{k-1}$ prove this subgroup is normal.

Reference for "Every finite $p$-group can be expressed as a section of a powerful $p$-group"

Is there any function in GAP finding all maximal elementary abelian subgroup of a $p$-group $P$?

Frattini subgroup of p-groups characteristics

How to find minimal generating sets efficiently?

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