Produkte von Gruppen mit endlichem torsionsfreien Rang (Q801038)

The following theorem is proved: Let the group G have a finite normal series with abelian or periodic factors. If the group \(G=AB\) is the product of two subgroups A and B with finite torsionfree ranks \(r_ 0(A)\) and \(r_ 0(B)\) and if the hypercenter of A has finite index in A, then G has finite torsionfree rank \(r_ 0(G)\leq r_ 0(A)+r_ 0(B)-r_ 0(A\cap B)\). - This generalizes a result of D. I. Zajtsev and uses some of his methods. It remains open whether the inequality can be replaced by equality.