ERRATA CORRIGE: Intrinsic algebraic entropy

TL;DR

This paper corrects a flaw in the proof of the Logarithmic Law for intrinsic algebraic entropy of Abelian group endomorphisms, ensuring the property holds as originally stated.

Contribution

It provides a valid proof of the Logarithmic Law for intrinsic algebraic entropy, fixing a previously identified flaw in the original argument.

Findings

The Logarithmic Law holds for intrinsic algebraic entropy.

A counterexample shows the original proof was flawed.

The corrected proof confirms the property’s validity.

Abstract

The notion of intrinsic algebraic entropy of an endomorphism of a given Abelian group has been recently introduced in [D. Dikranjan, A. Giordano Bruno, L. Salce, S. Virili, Intrinsic algebraic entropy, J. Pure Appl. Algebra 219 (2015) 2933-2961]. In this short note we provide a correct argument to prove one of the basic properties of the intrinsic algebraic entropy: the Logarithmic Law. In fact, this property was correctly stated in [op. cit.] but, as we will show with an explicit counterexample, the original proof contains a flaw.