Groups with the maximum condition on non-nilpotent subgroups

Abstract

In this paper the authors continue their study of groups with the maximum condition on non-nilpotent subgroups. Here the locally soluble-by-®nite groups G with this property are discussed. If G is not locally nilpotent then G is ®nitely generated and its Hirsch±Plotkin radical L is nilpotent. Furthermore GaL is abelian-by-®nite.

Groups with weak maximality condition for nonnilpotent subgroups

“…The notions of weak minimality and maximality conditions were introduced by Zaitsev [10] and Baer [11] and efficiently used in various investigations (see, e.g., the surveys [12,13]). After the cited Smith's work, a fairly detailed investigation of groups in which the family L nonnil (G) satisfies the maximality condition was carried out by Dixon and Kurdachenko [14,15]. Groups in which the family L nonnil (G) satisfies the minimality condition were studied by Dixon, Evans, and Smith [16].…”