Group of prime power order

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 $$p$$

Weaker properties

 * Nilpotent group:
 * Solvable group
 * Group whose order has at most two prime factors

Specific information
See groups of prime power order for more specific information.