The Group Properties Wiki (pre-alpha)

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From Groupprops

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

Contents 1 Definition 2 Relation with other properties 2.1 Stronger properties 2.2 Weaker properties

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^aq^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