Group of prime power order
The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter
View other prime-parametrized group properties | View other group properties
This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)
View other properties of finite groups OR View all group properties
A group of prime power order is defined in the following equivalent ways:
- It is a finite group whose order is a power of a prime.
- It is a finite group that is also a p-group for some prime : the order of every element is a power of that same prime
Equivalence of definitions
For full proof, refer: Equivalence of definitions of group of prime power order
Relation with other properties
- Nilpotent group: For full proof, refer: Prime power order implies nilpotent
- Solvable group
- Group whose order has at most two prime factors
See groups of prime power order for more specific information.