Formation (group theory)

In group theory, a branch of mathematics, 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. Gaschütz (1962) introduced formations to unify the theory of Hall subgroups and Carter subgroups 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.