On automorphisms of L(Z2 x SL(2, Z))

We will study the automorphisms on the group II1 factor L(Z(2) (?) SL (2, Z)) which preserve the subalgebra L(SL(2, Z)). Our main result is Out (L(Z(2) (?) SL(2, Z)), L(SL(2, Z))) similar or equal to Z(12) (?) Z(2), where Z(2) acts on Z(12) by the inverse operation. The proof is a modification of the recent paper due to Neshveyev and Stormer for non-commutative groups. The uniqueness of HT-Cartan subalgebras due to Popa plays a crucial role in the proof. (C) 2003 Elsevier Inc. All rights reserved.