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
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This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)
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Definition

Symbol-free definition

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 $p$: the order of every element is a power of that same prime $p$

Equivalence of definitions

For full proof, refer: Equivalence of definitions of group of prime power order

Relation with other properties

Weaker properties

• Nilpotent group: For full proof, refer: Prime power order implies nilpotent
• Solvable group
• Group whose order has at most two prime factors

Specific information

See groups of prime power order for more specific information.