# P-group

From Groupprops

## Contents

## Definition

Let be a prime. A -group is a group in which every element has finite order, and the order of every element is a power of .

The term -group is typically used for a *finite* -group, which is equivalent to a group of prime power order.

## Relation with other properties

### Stronger properties

- Group of prime power order
- Nilpotent p-group:
*For proof of the implication, refer and for proof of its strictness (i.e. the reverse implication being false) refer p-group not implies nilpotent*.