Rank of a p-group
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.