In mathematical group theory, a formation is a class of groups closed under taking images and such that if G/M and G/N are in the formation then so is G/M∩N. introduced formations to unify the theory of Hall subgroup

Hall subgroup

In mathematics, a Hall subgroup of a finite group G is a subgroup whose order is coprime to its index. They are named after the group theorist Philip Hall.- Definitions :A Hall divisor of an integer n is a divisor d of n such that...

s and Carter subgroup

Carter subgroup

In mathematics, especially in the field of group theory, a Carter subgroup of a finite group G is a subgroup H that is a nilpotent group, and self-normalizing...

s of finite solvable groups.

Some examples of formations are the formation of p-groups for a prime p, the formation of π-groups for a set of primes π, and the formation of nilpotent groups.

Schunck classes

A Schunck class, introduced by , is a generalization of a formation, consisting of a class of groups such that a group is in the class if and only if every primitive factor group is in the class. Here a group is called primitive if it has a self-centralizing normal abelian subgroup.