Groupprops, The Group Properties Wiki (pre-alpha)
TIP: Beware of terminology local to the wiki
ABOUT US: We use a Creative Commons license. All our content is free to reuse, with attribution. Learn more
ALSO CHECK OUT: Diffgeom: The Differential Geometry Wiki
Rank of a p-group
From Groupprops
Definition
The rank of a p-group is defined in the following equivalent ways:
- It is the maximum r for which there exists an elementary abelian subgroup of order pr.
- It is the maximum r for which there exists an abelian subgroup for which the minimum size of a generating set is r
For a finite p-group (i.e., a group of prime power order), the rank is finite.
This is also sometimes termed the depth of the p-group.
Related notions
