We prove that II1factors M have a unique (up to unitary conjugacy) cross-product type decomposition around "core subfactors" N ⊂ M satisfying the property HT of [S. Popa, On a class of type II1factors with Betti numbers invariants, Ann. of Math. (2) 163 (2006) 809-899] and a certain "torsion freeness" condition. In particular, this shows that isomorphism of factors of the form Lαi(Z2) ⋊ Fni, i = 1, 2, for Fni⊂ SL (2, Z) free groups of rank niand αj= e2 π itj, tj∉ Q, implies n1= n2. © 2006 Elsevier Inc. All rights reserved.
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