Finite solvable group

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

Definition

A finite group is termed a finite solvable group if it satisfies the following equivalent conditions:

• It is a solvable group
• It is a polycyclic group
• It has Sylow complements for all prime divisors of the order of the group
• It has Hall subgroups of all possible orders

Relation with other properties

Stronger properties

• Finite Abelian group
• Finite nilpotent group
• Finite supersolvable group