# Rank of a p-group

## Definition

The rank of a p-group is defined in the following equivalent ways:

- It is the maximum for which there exists an elementary abelian subgroup of order .
- It is the maximum for which there exists an abelian subgroup for which the minimum size of a generating set is

For a finite -group (i.e., a group of prime power order), the rank is finite.

This is also sometimes termed the **depth** of the p-group.