A finiteness condition on subgroups of large derived length

Abstract

The authors discuss the class S d (r) of groups in which every finitely generated subgroup is either at most r-generated or soluble of derived length at most d. Such groups need not be of finite rank or soluble of derived length at most d in general. A structure theorem is obtained for locally finite, and for certain locally nilpotent, S d (r)-groups.  2004 Elsevier Inc. All rights reserved.