Generalized nilpotent group

A group in one of the generalized nilpotent classes of groups. A class of groups is called generalized nilpotent if it contains all nilpotent groups (cf. Nilpotent group) and if its intersection with the class of finite groups is the class of all finite nilpotent groups. Quite a number of classes of generalized nilpotent groups have been considered; principally, the connections between them have been studied. The most important classes of generalized nilpotent groups are the class of locally nilpotent groups (cf. Locally nilpotent group), and the classes of nil groups (cf. Nil group), Engel groups (cf. Engel group) and groups with a normalizer condition. The majority of classes of generalized nilpotent groups were introduced in studying various properties of central or normal series and systems of subgroups (see [1], [2]).

References

[1]	A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian)
[2]	A.G. Kurosh, S.N. Chernikov, "Solvable and nilpotent groups" Uspekhi Mat. Nauk , 2 : 3 (1947) pp. 18–59 (In Russian)

References

[a1]	D.J.S. Robinson, "Finiteness condition and generalized soluble groups" , 1–2 , Springer (1972)
[a2]	D.J.S. Robinson, "A course in the theory of groups" , Springer (1980)