Abstract
We give new examples of FA presentable torsion-free abelian groups. Namely, for every n ≥ 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 (ℤ, + )2 in which every nontrivial cyclic subgroup is not FA recognizable.
This research was partially supported by the Marsden Fund of New Zealand, grant no. 03-UOA-130.
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References
Arnold, D.: Finite Rank Torsion Free Abelian Groups and Rings. Springer, Heidelberg (1982)
Blumensath, A., Grädel, E.: Automatic structures. In: 15th Annual IEEE Symposium on Logic in Computer Science, Santa Barbara, CA, 2000, pp. 51–62. IEEE Comput. Soc. Press, Los Alamitos (2000)
Delhommé, C.: Non-automaticity of ω ω. Manuscript (2001)
Fuchs, L.: Infinite Abelian Groups, vol. 1, 2. Academic Press, London (1970, 1973)
Hodgson, B.R.: Théories décidables par automate fini. PhD Thesis, University of Montreal (1976)
Hodgson, B.R.: Théories décidables par automate fini. Annales de Sciences Mathématiques 7, 39–57 (1983)
Khoussainov, B., Neorde, A.: Automatic presentations of structures. In: Leivant, D. (ed.) LCC 1994. LNCS, vol. 960, pp. 367–392. Springer, Heidelberg (1995)
Khoussainov, B., Rubin, S.: Automatic structures: overview and future directions. J. Autom. Lang. Comb. (Weighted automata: theory and applications, Dresden, 2002) 8(2), 287–301 (2003)
Khoussainov, B., Nies, A., Rubin, S., Stephan, F.: Automatic structures: richness and limitations. In: Proceedings of the 19th IEEE Symposium on Logic in Computer Science, pp. 110–119. IEEE Computer Society Press, Los Alamitos (2004)
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Nies, A., Semukhin, P. (2007). Finite Automata Presentable Abelian Groups . In: Artemov, S.N., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2007. Lecture Notes in Computer Science, vol 4514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72734-7_29
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DOI: https://doi.org/10.1007/978-3-540-72734-7_29
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