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Let G = (a) xi X where (a) is a cyclic group of order n , X is an abelian group of order m , and (n, m) = 1 . We prove that if ZG is the integral group ring of G and H is a finite group of units of augmentation one of liG , then there exists a rational unit y such that fl'CC.doi:10.1090/s0002-9939-1994-1186996-9 fatcat:tjdbeib6d5ag7jyyesowzfpasi