Groups with Bounded Chernikov Conjugate Classes of Elements
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).
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 6, pp 979-989.
Citation Example: Kurdachenko L. A., Otal J., Subbotin I. Ya. Groups with Bounded Chernikov Conjugate Classes of Elements // Ukr. Mat. Zh. - 2002. - 54, № 6. - pp. 798-807.