The subnormal coalescence of some classes of groups of finite rank

Abstract

A class of groups forms a (subnormal) coalition class, or is (subnormally) coalescent, if wheneverHandKare subnormal -subgroups of a groupGthen their join <H, K> is also a subnormal -subgroup ofG. Among the known coalition classes are those of finite groups and polycylic groups (Wielandt [15]); groups with maximal condition for subgroups (Baer [1]); finitely generated nilpotent groups (Baer [2]); groups with maximal or minimal condition on subnormal subgroups (Robinson [8], Roseblade [11, 12]); minimax groups (Roseblade, unpublished); and any subjunctive class of finitely generated groups (Roseblade and Stonehewer [13]).