Formation (group theory)

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 :1 \rightarrow A \rightarrow B \rightarrow C \rightarrow 1\ A and C are in M if and only if B is in M. A full formation is a Melnikov formation which is also closed under taking subgroups. An almost full formation is one which is closed under quotients, direct products and subgroups, but not necessarily extensions. The families of finite abelian groups and finite nilpotent groups are almost full, but neither full nor Melnikov. ==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. == Notes ==