Characterization of groups with generalized Chernikov periodic part (Q1581441)

A Chernikov group is a finite extension of a direct product of finitely many quasicyclic groups. A generalized Chernikov group \(G\) is an extension of a direct product \(A\) of quasicyclic \(p\)-groups with finitely many factors for each prime \(p\) by a locally normal group \(B\), where each element of \(G\) is element-wise permutable with all but a finite number of primary Sylow subgroups of \(A\). The author considers groups in which the elements with finite order form a generalized Chernikov group. Using earlier results of his he characterizes these groups in particular under the condition that there are no elements of order \(2\).