# Category:Cyclic Groups

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This category contains results about **Cyclic Groups**.

Definitions specific to this category can be found in Definitions/Cyclic Groups.

The group $G$ is **cyclic** if and only if every element of $G$ can be expressed as the power of one element of $G$:

- $\exists g \in G: \forall h \in G: h = g^n$

for some $n \in \Z$.

## Subcategories

This category has the following 15 subcategories, out of 15 total.

### C

- Cyclic Group is Abelian (3 P)
- Cyclic Group of Order 3 (5 P)
- Cyclic Group of Order 8 (2 P)

### E

### G

- Group of Order p q is Cyclic (4 P)

### P

### Q

### S

## Pages in category "Cyclic Groups"

The following 54 pages are in this category, out of 54 total.

### A

### C

### E

### F

### G

- 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 of Order 15 is Cyclic Group
- Group of Order 35 is Cyclic Group
- Group of Order p q is Cyclic
- Group Presentation of Cyclic Group
- Group whose Order equals Order of Element is Cyclic
- Groups of Order 2p