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

2009/05/10 by Tsankov, Todor · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.0905.1505

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 Q/Z. The proof is combinatorial and uses most notably Freiman's theorem on sets with small doubling.

Cited by

• Simple Classes of Automatic Structures

Related

• Embedding ℚ into a Finitely Presented Group
• Presentations of finite simple groups: a computational approach
• Presentations of finite simple groups: a quantitative approach
• Non-congruence presentations of finite simple groups
• Presentations for P^K