2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70086We obtain an estimate of Voiculescu's (modified) free entropy dimension for generators of a ${II}_1$-factor $\mc{M}$ with a subfactor $\mc{N}$ containing an abelian subalgebra $\mc{A}$ of finite multiplicity. It implies in particular that the interpolated free group subfactors of finite Jones index do not have abelian subalgebras of finite multiplicity or Cartan subalgebras.Operator Algebras46Lxx (Primary) 47Lxx (Secondary)text