  We prove that the normalizer of any diffuse amenable subalgebra of a free
group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra.
Moreover, any II$_1$ factor of the form $Q \vt L(\Bbb F_r) $, with $Q$ an
arbitrary subfactor of a tensor product of free group factors, has no Cartan
subalgebras. We also prove that if a free ergodic measure preserving action of
a free group $\Bbb F_r$, $2\leq r \leq \infty$, on a probability space
$(X,\mu)$ is profinite then the group measure space factor $L^\infty(X)\rtimes
\Bbb F_r$ has unique Cartan subalgebra, up to unitary conjugacy.
