Question

Which finite abelian groups contain the group of units of some integer as a direct summand?

score 57 · Answer 1 · 2026-04-12 19:42:49

57

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Which finite abelian groups contain the group of units of some integer as a direct summand?

Published on 12 Apr 2026 - 19:42

score 119 · Answer 2 · 2026-04-10 14:16:18

119

Views

When does the subgroup generated by a generator of a group admit a complement?

Published on 10 Apr 2026 - 14:16

score 402 · Answer 3 · 2026-04-14 23:28:19

402

Views

For every element $g$ in a group $G$ of order $23$, there is $h\in G$ such that $g=h^2$.

Published on 14 Apr 2026 - 23:28

score 71 · Answer 4 · 2026-04-12 00:21:13

71

Views

Counting the matrix groups isomorphic to a finite group

Published on 12 Apr 2026 - 0:21

score 346 · Answer 5 · 2026-04-15 02:10:20

346

Views

Action of $\text{PSL}(2,q)$ on the projective line: How to know if $(az+b)/(cz+d)$ belongs to $\text{PSL}(2,q$)?

Published on 15 Apr 2026 - 2:10

score 49 · Answer 6 · 2026-04-17 00:31:13

49

Views

Prove that $[G: S]=[\phi [G]: \phi [S]] \cdot[N: S \cap N]$

Published on 17 Apr 2026 - 0:31

score 592 · Answer 7 · 2026-04-12 06:47:33

592

Views

Abelian finite groups and their subgroups

Published on 12 Apr 2026 - 6:47

score 56 · Answer 8 · 2026-03-26 04:14:38

56

Views

$G= \langle a, b : a^{7} = b^{3} = 1,\ b^{-1}ab = a^{2} \rangle$ and commutator group

Published on 26 Mar 2026 - 4:14

score 394 · Answer 9 · 2026-04-13 23:57:53

394

Views

Does the center of a perfect group not contain all elements of prime order?

Published on 13 Apr 2026 - 23:57

score 434 · Answer 10 · 2026-04-12 15:09:08

434

Views

Is it possible to have $\sum_{g\in G} \chi(g)=\frac{1}{2}$?

Published on 12 Apr 2026 - 15:09

score 192 · Answer 11 · 2026-04-14 16:04:00

192

Views

On wreath product of finite $p$-groups

Published on 14 Apr 2026 - 16:04

score 73 · Answer 12 · 2026-04-15 05:52:10

73

Views

A group of even order contains an element of order 2 : a proof by contradiction.

Published on 15 Apr 2026 - 5:52

score 113 · Answer 13 · 2026-04-15 15:28:22

113

Views

Each permutation in permutation group PSL2 consist of fixed points and cycles of equal lengths. Prove or disprove it.

Published on 15 Apr 2026 - 15:28

score 437 · Answer 14 · 2026-03-25 12:50:13

437

Views

Let $G$ be a finite nilpotent group and $G'$ its commutator subgroup. Show that if $G/G'$ is cyclic then $G$ is cyclic.

Published on 25 Mar 2026 - 12:50

score 60 · Answer 15 · 2026-04-10 06:05:34

60

Views

Picking the set of coset representatives of a stabilizer under a group action

Published on 10 Apr 2026 - 6:05

List Question

Which finite abelian groups contain the group of units of some integer as a direct summand?

When does the subgroup generated by a generator of a group admit a complement?

For every element $g$ in a group $G$ of order $23$, there is $h\in G$ such that $g=h^2$.

Counting the matrix groups isomorphic to a finite group

Action of $\text{PSL}(2,q)$ on the projective line: How to know if $(az+b)/(cz+d)$ belongs to $\text{PSL}(2,q$)?

Prove that $[G: S]=[\phi [G]: \phi [S]] \cdot[N: S \cap N]$

Abelian finite groups and their subgroups

$G= \langle a, b : a^{7} = b^{3} = 1,\ b^{-1}ab = a^{2} \rangle$ and commutator group

Does the center of a perfect group not contain all elements of prime order?

Is it possible to have $\sum_{g\in G} \chi(g)=\frac{1}{2}$?

On wreath product of finite $p$-groups

A group of even order contains an element of order 2 : a proof by contradiction.

Each permutation in permutation group PSL2 consist of fixed points and cycles of equal lengths. Prove or disprove it.

Let $G$ be a finite nilpotent group and $G'$ its commutator subgroup. Show that if $G/G'$ is cyclic then $G$ is cyclic.

Picking the set of coset representatives of a stabilizer under a group action

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