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.
A Melnikov formation is closed under taking quotients, normal subgroups and group extensions.
[1] An almost full formation is one which is closed under quotients, direct products and subgroups, but not necessarily extensions.
Here a group is called primitive if it has a self-centralizing normal abelian subgroup.