On a subfactor generalization of Wall's conjecture

In this paper we discuss a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. We explore special cases of this conjecture and present supporting evidence. In particular we prove special cases of this conjecture related to some finite dimensional Kac Algebras of Izumi-Kosaki type which include relative version of Wall's conjecture for solvable groups.