Finitely Presented MV-algebras with Finite Automorphism Group

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 restrict attention to finitely presented MV-algebras. Recall that an MV-algebra is finitely presented if it is (isomorphic to) a quotient of a free finitely generated MV-algebra by a finitely generated ideal. If M is a finitely generated MV-algebra, the collection μ(M) of its maximal ideals, endowed with the Zariski (or hull-kernel) topology, is a compact Hausdorff space called the maximal spectrum of M . The space μ(M) is homeomorphic to a closed subspace of the real unit n-cube [0, 1], for some nonnegative integer n. We denote by dim μ(M) the (Hausdorff topological) dimension of μ(M). (Please see [3, Chapter 7] for background on dimension theory.)