Locally finite minimal non-FC-groups

1989-5
Kuzucuoglu, Mahmut
Phillips, Richard E.
We recall that a group G is an FC-group if for every x∈G the set of conjugates {xg|g∈G} is a finite set. Our interest here is with those groups G which are not FC groups while every proper subgroup of G is an FC-group: such groups are called minimal non-FC-groups. Locally finite minimal non-FC-groups with (G ≠ G′ are studied in [1] and the structure of these groups is reasonably well understood. In [2] Belyaev has shown that a perfect, locally finite, minimal non-FC-group is either a simple group or a p-group for some prime p. Here we make use of the results of [5] to refine the result of Belyaev and provide a positive answer to problem 5·1 of [11]; in particular, we prove the following

Citation Formats
M. Kuzucuoglu and R. E. Phillips, “Locally finite minimal non-FC-groups,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 105, no. 3, pp. 417–420, 1989, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51734.