Groups with Bounded Chernikov Conjugate Classes of Elements

Abstract

We consider BCC-groups, that is groups G with Chernikov conjugacy classes in which for every element x ∈ G the minimax rank of the divisible part of the Chernikov group G/C _G(x ^G) and the order of the corresponding factor-group are bounded in terms of G only. We prove that a BCC-group has a Chernikov derived subgroup. This fact extends the well-known result due to B. H. Neumann characterizing groups with bounded finite conjugacy classes (BFC-groups).