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- Title
GROUPS WHOSE GEODESICS ARE LOCALLY TESTABLE.
- Authors
HERMILLER, SUSAN; HOLT, DEREK F.; REES, SARAH; Mangolis, S.
- 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 1-locally testable 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.
- Subjects
GEODESICS; ABELIAN groups; SET theory; TORSION products; CONJUGACY classes; CELLULAR automata
- Publication
International Journal of Algebra & Computation, 2008, Vol 18, Issue 5, p911
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196708004676