formation

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. 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. Special cases A Melnikov formation is closed under taking quotients, normal subgroups and group extensions. Thus a Melnikov formation M has the property that for every short exact sequence A and C are in M if and only if B is in M.