On a subfactor generalization of Wallʼs conjecture

In this paper we discuss a conjecture on intermediate subfactors which is a generalization of Wallʼs 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 Wallʼs conjecture for solvable groups.