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We determine properties of Boolean powers of groups and other algebraic structures, and we generalize Jonsson's theorem on Boolean powers of centerless, directly indecomposable groups. We show that every nonabelian, finitely generated group has 2*° nonisomorphic countable Boolean, and hence subcartesian, powers. We show that nonabelian groups G such that either (i) G is not the central product of two nonabelian groups or (ii) every pair of nontrivial normal subgroups of G intersect nontrivially yield nonisomorphic Boolean powers with respect to nonisomorphic Boolean algebras. Summary. We determine properties of Boolean powers of groups and other algebraic structures in the spirit of Jonsson [4] and Lawrence [6]. In §1 our main theorem concerns direct decompositions of Boolean powers and generalizes in a functorial setting Jonsson's well-known theorem on Boolean powers of centerless indecomposable groups. In §2 we show that every nonabelian, finitely generated group has 2"° nonisomorphic countable Boolean, and hence subcartesian, powers. (For regular k > X0 the existence of 2" mutually nonembeddable subcartesian powers of power k of every nonabelian group of power G be

Boolean powers: direct decomposition and isomorphism types