BREAKING UP FINITE AUTOMATA PRESENTABLE TORSION-FREE ABELIAN GROUPS

作者：Braun Gabor^*; Struengmann Lutz

来源：International Journal of Algebra and Computation, 2011, 21(8): 1463-1472.

DOI：10.1142/S0218196711006625

• FA-presentable abelian groups
• automatic structures
• additive combinatorics

In [Todor Tsankov, The additive group of the rationals does not have an automatic presentation, May 2009, arXiv:0905.1505v1], it was shown that the group of rational numbers is not FA-presentable, i.e. it does not admit a presentation by a finite automaton. More generally, any torsion-free abelian group that is divisible by infinitely many primes is not of this kind. In this article we extend the result from [13] and prove that any torsion-free FA-presentable abelian group G is an extension of a finite rank free group by a finite direct sum of Prufer groups Z(p(infinity)).

• 出版日期2011-12