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).
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Kurdachenko, L.A., Otal, J. & Subbotin, I.Y. Groups with Bounded Chernikov Conjugate Classes of Elements. Ukrainian Mathematical Journal 54, 979–989 (2002). https://doi.org/10.1023/A:1021716421009
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DOI: https://doi.org/10.1023/A:1021716421009