View source for 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|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|Locally nilpotent group]]), and the classes of nil groups (cf. [[Nil group|Nil group]]), Engel groups (cf. [[Engel group|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 [[#References|[1]]], [[#References|[2]]]).

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.G. Kurosh,   "The theory of groups" , '''1–2''' , Chelsea  (1955–1956)  (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  A.G. Kurosh,   S.N. Chernikov,   "Solvable and nilpotent groups"  ''Uspekhi Mat. Nauk'' , '''2''' :  3  (1947)  pp. 18–59  (In Russian)</TD></TR></table>



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  D.J.S. Robinson,   "Finiteness condition and generalized soluble groups" , '''1–2''' , Springer  (1972)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  D.J.S. Robinson,   "A course in the theory of groups" , Springer  (1980)</TD></TR></table>