Realization of saturated transfer systems on cyclic groups of order \(p^nq^m\) by linear isometries \(N_\infty \)-operads

We prove a specific case of Rubin’s saturation conjecture about the realization of G-transfer systems, for G a finite cyclic group, by linear isometries \(N_\infty \)-operads, namely the case of cyclic groups of order \(p^nq^m\) for p, q distinct primes and \(n,m\in \mathbb {N}\).