Published online by Cambridge University Press: 20 November 2018
Let be a class of groups which is closed under the forming of subgroups, epimorphic images and extensions. It is shown that every soluble product G = AB of two -subgroups A and B, one of which satisfies max or min, is an -group (Theorem A). If X satisfies an additional requirement, then every soluble product G = AB of two -subgroups A and B, one of which is a torsion group with min-p for every prime p, is an -group (Theorem B). Corollary: Every soluble product G = AB of two π-subgroups A and B with min-p for every prime p in the set of primes π, is a π -group with min-p for every p.