  Let $\Gamma$ be a countable group and let $\Gamma_0$ be an infinite abelian
subgroup of $\Gamma$. We prove that if the pair $(\Gamma,\Gamma_0)$ satisfies
some combinatorial condition called (SS), then the abelian subalgebra
$A=L(\Gamma_0)$ is a singular MASA in $M=L(\Gamma)$ which satisfies a weakly
mixing condition. If moreover it satisfies a stronger condition called (ST),
then it provides a singular MASA with a strictly stronger mixing property. We
describe families of examples of both types coming from free products, HNN
extentions and semidirect products, and in particular we exhibit examples of
singular MASA's that satisfy the weak mixing condition but not the strong
mixing one.
