FACTORIAL DIVISIBLE ABELIAN GROUPS WITH RESTRICTIONS ON SYSTEMS OF FACTOR GROUPS

Factorial divisible groups were introduced by Beaumont and Peirce for the case of torsion-free groups in 1961 and generalized to all groups by Wickles and A. A. Fomin in 1998. In this paper, we study quotient divisible Abelian groups whose quotient group is a quotient divisible group of rank 1. It is proposed to study the properties of such groups using cocharacteristics and cotypes. The properties of cocharacteristics and cotypes are obtained, and sufficient conditions are found for a normal subgroup whose quotient group is quotient divisible of rank 1 to be distinguished in a quotient divisible group as a direct summand, which contributes to further study of the structure of groups.