On the theory of groups with the minimality condition (Q1337842)

In the investigation of groups with minimum condition for subgroups one often encounters ``quasi-Chernikov groups'', i.e. groups which are not Chernikov groups, but all their proper subgroups are. Recall that a Chernikov group is an abelian-by-finite group with minimum condition. Here a number of important properties about the intersections of infinite maximal Chernikov subgroups of a simple quasi-Chernikov group without involutions are derived.