Question

Do some cyclic subgroups "partition" a group?

score 254 · Answer 1 · 2026-03-29 15:53:10

254

Views

Do some cyclic subgroups "partition" a group?

Published on 29 Mar 2026 - 15:53

score 73 · Answer 2 · 2026-04-01 09:08:29

73

Views

Classifying $\operatorname{Aut}(\mathbb{Z}_n)$ in terms of $\mathbb{Z}_k$.

Published on 01 Apr 2026 - 9:08

score 124 · Answer 3 · 2021-09-15 12:05:20

124

Views

Why is $n \ge 2$ not mentioned instead of $n \ge 3$ in $(\mathbb{Z}/2^n \mathbb{Z})^{\times}?$

Published on 15 Sep 2021 - 12:05

score 78 · Answer 4 · 2021-09-17 08:25:17

78

Views

What is the relation between extending $\varphi_a$ to an isomorphism and finding the generators of $\mathbb Z_{48}$?

Published on 17 Sep 2021 - 8:25

score 52 · Answer 5 · 2021-09-19 07:23:14

52

Views

How many elements of a cyclic groups of order $n$ are generators for that group?

Published on 19 Sep 2021 - 7:23

score 439 · Answer 6 · 2026-04-04 06:18:51

439

Views

Find the number of group homomorphisms from $\mathbb{Z}_8$ to $S_3$.

Published on 04 Apr 2026 - 6:18

score 71 · Answer 7 · 2026-03-28 09:57:36

71

Views

Suppose $M\leq P$ such that $|M|=p^m$, and both $M$ and $P/M$ are cyclic, then there exists $N\leq P$ such that $P=M+N$ and $M\cap N=\{0\}$.

Published on 28 Mar 2026 - 9:57

score 205 · Answer 8 · 2021-09-27 22:58:03

205

Views

General rule to say that $(\mathbb{Z}/n \mathbb{Z})^{\times}$ is cyclic

Published on 27 Sep 2021 - 22:58

score 188 · Answer 9 · 2026-03-28 03:58:41

188

Views

Prove that if a subgroup $H$ generated by $x$ is of infinity order, then $H=\langle x^a\rangle$ iff $a = ±1$

Published on 28 Mar 2026 - 3:58

score 3.6k · Answer 10 · 2021-10-01 00:28:57

3.6k

Views

Prove or disprove that if every proper subgroup $G$ is cyclic, then $G$ is cyclic.

Published on 01 Oct 2021 - 0:28

score 447 · Answer 11 · 2021-10-02 15:13:07

447

Views

Prove that every group of order $595$ is cyclic.

Published on 02 Oct 2021 - 15:13

score 178 · Answer 12 · 2021-10-03 15:56:53

178

Views

Prove that every finite group is generated by its cyclic subgroups.

Published on 03 Oct 2021 - 15:56

score 478 · Answer 13 · 2021-10-10 18:47:14

478

Views

Is the group $\mathbb Z/3 \times \mathbb Z/5$ cyclic?

Published on 10 Oct 2021 - 18:47

score 127 · Answer 14 · 2026-04-01 12:10:09

127

Views

Automorphisms, Cyclic Groups, and Order

Published on 01 Apr 2026 - 12:10

score 267 · Answer 15 · 2026-04-05 19:01:52

267

Views

How do I find my composition law?

Published on 05 Apr 2026 - 19:01

List Question

Do some cyclic subgroups "partition" a group?

Classifying $\operatorname{Aut}(\mathbb{Z}_n)$ in terms of $\mathbb{Z}_k$.

Why is $n \ge 2$ not mentioned instead of $n \ge 3$ in $(\mathbb{Z}/2^n \mathbb{Z})^{\times}?$

What is the relation between extending $\varphi_a$ to an isomorphism and finding the generators of $\mathbb Z_{48}$?

How many elements of a cyclic groups of order $n$ are generators for that group?

Find the number of group homomorphisms from $\mathbb{Z}_8$ to $S_3$.

Suppose $M\leq P$ such that $|M|=p^m$, and both $M$ and $P/M$ are cyclic, then there exists $N\leq P$ such that $P=M+N$ and $M\cap N=\{0\}$.

General rule to say that $(\mathbb{Z}/n \mathbb{Z})^{\times}$ is cyclic

Prove that if a subgroup $H$ generated by $x$ is of infinity order, then $H=\langle x^a\rangle$ iff $a = ±1$

Prove or disprove that if every proper subgroup $G$ is cyclic, then $G$ is cyclic.

Prove that every group of order $595$ is cyclic.

Prove that every finite group is generated by its cyclic subgroups.

Is the group $\mathbb Z/3 \times \mathbb Z/5$ cyclic?

Automorphisms, Cyclic Groups, and Order

How do I find my composition law?

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