Malnormal subgroups of lattices and the Pukanszky invariant in group factors

Abstract

Let $G$ be a connected semisimple real algebraic group. Assume that $G(\bb R)$ has no compact factors and let $\Gamma$ be a torsion-free uniform lattice subgroup of $G(\bb R)$. Then $\Gamma$ contains a malnormal abelian subgroup $A$. This implies that the $\tto$ factor $\vn(\Gamma)$ contains a masa $\fk A$ with Puk\'anszky invariant $\{\infty\}$.