Saturated and linear isometric transfer systems for cyclic groups of order pq

Transfer systems are combinatorial objects which classify N∞ operads up to homotopy. By results of A. Blumberg and M. Hill [2], every transfer system associated a linear isometries operad is also saturated (closed under particular two-out-of-three property). We investigate isometric with equivariance group Cpmqn, the cyclic order pmqn for p,q distinct primes m,n≥0. give complete enumeration Cpmqn. prove J. Rubin's saturation conjecture Cpqn; this says that realized by sufficiently large (greater than 3 in case).