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

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

2009-05-10

arxiv.org/abs/0905.1505v1

Mathematics

Logic

11 pages

Scientific paper

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.

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