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- W2950249979 abstract "A regular set of words is ($k$-)locally testable if membership of a word in the set is determined by the nature of its subwords of some bounded length $k$. In this article we study groups for which the set of all geodesic words with respect to some generating set is ($k$-)locally testable, and we call such groups ($k$-)locally testable. We show that a group is klt{1} if and only if it is free abelian. We show that the class of ($k$-)locally testable groups is closed under taking finite direct products. We show also that a locally testable group has finitely many conjugacy classes of torsion elements. Our work involved computer investigations of specific groups, for which purpose we implemented an algorithm in GAP to compute a finite state automaton with language equal to the set of all geodesics of a group (assuming that this language is regular), starting from a shortlex automatic structure. We provide a brief description of that algorithm." @default.
- W2950249979 created "2019-06-27" @default.
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- W2950249979 date "2011-11-03" @default.
- W2950249979 modified "2023-10-16" @default.
- W2950249979 title "Groups whose geodesics are locally testable" @default.
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- W2950249979 doi "https://doi.org/10.48550/arxiv.1111.0775" @default.
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