Multiplication groups of quotient divisible Abelian groups

A multiplication on an Abelian group G is a homomorphism mu : G circle times G -> G. The set Mult G of all multiplications on an Abelian group G itself is an Abelian group with respect to addition; this group is called the multiplication group of G. In the paper, the class QD1 of quotient divisible Abelian groups of rank 1 is considered. The group Mult G is described for G is an element of QD1. In the group Mult G, multiplications defining comparable rings on G are described for any group G is an element of QD1. The isomorphism problem is solved in QD1: multiplications defining isomorphic rings on G are described for any G is an element of QD1.