On finitely generated submonoids of virtually free groups
Group Theory
2018-05-22 v2 Formal Languages and Automata Theory
Abstract
We prove that it is decidable whether or not a finitely generated submonoid of a virtually free group is graded, introduce a new geometric characterization as quasi-geodesic monoids, and show that their word problem is rational (as a relation). We also solve the isomorphism problem for this class of monoids, generalizing earlier results for submonoids of free monoids. We also prove that the classes of graded monoids, regular monoids and Kleene monoids coincide for submonoids of free groups.
Keywords
Cite
@article{arxiv.1712.07746,
title = {On finitely generated submonoids of virtually free groups},
author = {Pedro V. Silva and Alexander Zakharov},
journal= {arXiv preprint arXiv:1712.07746},
year = {2018}
}
Comments
22 pages. Main results generalized to virtually free groups, new geometric characterisation added in Section 4, Section 6 modified to include word problem for monoids, main proofs shortened, references added