The Pinsker subgroup of an algebraic flow

The algebraic entropy h defined for endomorphisms ϕ of abelian groups G measures the growth of the trajectories of non-empty finite subsets F of G with respect to ϕ. We show that this growth can be either polynomial or exponential. The greatest ϕ-invariant subgroup of G where this growth is polynomial coincides with the greatest ϕ-invariant subgroup of G (named Pinsker subgroup of ϕ) such that . We obtain also an alternative characterization of from the point of view of the quasi-periodic points of ϕ.