Growth rate for endomorphisms of finitely generated nilpotent groups

Abstract

We prove that the growth rate of an endomorphism of a finitely generated nilpotent group is equal to the growth rate of the induced endomorphism on its abelianization, generalizing the corresponding result for an automorphism in [T. Koberda, Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups, In the Tradition of Ahlfors-Bers. VI, Contemp. Math. 590, American Mathematical Society, Providence 2013, 87-99].