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Finite automata presentable abelian groups. (English) Zbl 1133.68050
Artemov, Sergei N. (ed.) et al., Logical foundations of computer science. International symposium, LFCS 2007, New York, NY, USA, June 4–7, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-72732-3/pbk). Lecture Notes in Computer Science 4514, 422-436 (2007).
Summary: We give new examples of FA presentable torsion-free abelian groups. Namely, for every \(n \geq 2\), we construct a rank \(n\) indecomposable torsion-free abelian group which has an FA presentation. We also construct an FA presentation of the group \((\mathbb Z, + )^{2}\) in which every nontrivial cyclic subgroup is not FA recognizable.
For the entire collection see [Zbl 1121.03005].

68Q70 Algebraic theory of languages and automata
03D05 Automata and formal grammars in connection with logical questions
20K15 Torsion-free groups, finite rank
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