Abstract
Neumann characterized the groups in which every subgroup has finitely many conjugates only as central-by-finite groups. If 𝔛 is a class of groups, a group G is said to have 𝔛-conjugate classes of subgroups if G/Core G (N G (H)) ∈ 𝔛 for every subgroup H of G. In this paper, we generalize Neumann's result by showing that a group has polycyclic-by-finite classes of conjugate subgroup if and only if it is central-by-(polycyclic-by-finite).
Key Words:
Acknowledgment
The authors wish to thank the referee for his/her useful suggestions, which have allowed to improve this paper. This research was supported by Proyecto BFM2001-2452 of CICYT (Spain), Proyecto 100/2001 of Gobierno de Aragón (Spain) and the University of Athens-R.C., grant No 3403.
Notes
#Communicated by M. Dixon.