Group whose order has at most two prime factors

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

A group whose order has at most two prime factors is a finite group such that there are at most two prime numbers which divide the order of the group. In other words, the order of the group has the form $p^{a}q^{b}$ where $p,q$ are prime numbers and $a,b$ are nonnegative integers.

Relation with other properties

Stronger properties

• Trivial group
• Group of prime power order
• Shmidt group

Weaker properties

• Solvable group: For full proof, refer: Order has only two prime factors implies solvable