# Category:Cyclic Groups

From ProofWiki

This category contains results about Cyclic Groups.

The group $G$ is **cyclic** if and only if there exists $g \in G$ such that for every $h \in G$, $h = g^n$ for some integer $n$, where:

- $g^n$ is the $n$th power of $g$

## Subcategories

This category has the following 6 subcategories, out of 6 total.

### C

### E

### G

### P

### Q

### S

## Pages in category "Cyclic Groups"

The following 37 pages are in this category, out of 37 total.

### C

### E

### F

### G

- Generator of Cyclic Group is not Unique
- Generators of Additive Group of Integers
- Generators of Infinite Cyclic Group
- Group Direct Product of Cyclic Groups
- Group Direct Product of Cyclic Groups/Corollary
- Group Direct Product of Infinite Cyclic Groups
- Group whose Order equals Order of Element is Cyclic