The additive group of the rationals does not have an automatic presentation

Abstract

We prove that the additive group of the rationals does not have an automatic presentation. The proof also applies to certain other abelian groups, for example, torsion-free groups that are p-divisible for infinitely many primes p, or groups of the form ⊕_{p ∈ I} Z(p^∞), where I is an infinite set of primes.