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 R (direct X)-bar L F_(r_1) (direct X)-bar…(direct X)-bar L F_(r_m) is isomorphic to a subfactor in R (direct X)-bar L F_(s_1) (direct X)-bar…(direct X) L F_(sn), for some 2 ≤ r_i, s_j ≤ ∞ then m ≤ n.
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机译：我们证明了来自类型II1因子张量积的几个独特的素因数分解结果，这些结果来自可以实现为双曲组的子组或实秩为1的相连Lie组的离散子组的组。特别是，我们证明了如果R（ X）-bar L F_（r_1）（直接X）-bar…（直接X）-bar L F_（r_m）与R（直接X）-bar L F_（s_1）（direct X）- bar…（直接X）L F_（sn），对于2≤r_i，s_j≤∞，则m≤n。
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