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

Todor Tsankov

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arXiv · 0905.1505

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

Todor Tsankov

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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.

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BibTeX RIS

Todor Tsankov. 2009-05-10. The additive group of the rationals does not have an automatic presentation. https://arxiv.org/abs/0905.1505

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