Please see [1] for background on MV-algebras. We address the question, which MV-algebras have finite automorphism group. The automorphism group of the free MV-algebra on 1 generator is just the group of order 2 (folklore). In contrast, it is known that the automorphism group of the free MV-algebra on 2 generators is not even locally finite [4, 2]. Not much else seems to be known. Let us restric...