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

Abstract 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 $$N_\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> -operads, namely the case of cyclic groups of order $$p^nq^m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>m</mml:mi> </mml:msup> </mml:mrow> </mml:math> for p , q distinct primes and $$n,m\in \mathbb {N}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> .