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.
Popa, S. (2007). A unique decomposition result for HT factors with torsion free core. Journal of Functional Analysis, 242(2), 519–525. https://doi.org/10.1016/j.jfa.2006.05.016