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Abstract: We prove that the additive group of the rationals does not have an automaticpresentation. The proof also applies to certain other abelian groups, forexample, torsion-free groups that are $p$-divisible for infinitely many primes$p$, or $Q-Z$. The proof is combinatorial and uses most notably Freiman-stheorem on sets with small doubling.



Autor: Todor Tsankov

Fuente: https://arxiv.org/







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