Some prime factorization results for type II1 factors

We prove several unique prime factorization results for tensor products of type II1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected Lie groups of real rank 1. In particular, we show that if Rcircle timesLF(r 1) circle times...circle times LFr m is isomorphic to a subfactor in Rcircle timesLF(s 1) circle times...circle times LFs n, for some 2less than or equal tor(i), s(j)less than or equal toinfinity, then mless than or equal ton.