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On finitely generated submonoids of virtually free groups

On finitely generated submonoids of virtually free groups AbstractWe prove that it is decidable whether or not a finitely generated submonoid of a virtually free group is graded, introduce a new geometric characterization of graded submonoids in virtually free groups as quasi-geodesic submonoids, 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

On finitely generated submonoids of virtually free groups

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Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6104
eISSN
1869-6104
DOI
10.1515/gcc-2018-0008
Publisher site
See Article on Publisher Site

Abstract

AbstractWe prove that it is decidable whether or not a finitely generated submonoid of a virtually free group is graded, introduce a new geometric characterization of graded submonoids in virtually free groups as quasi-geodesic submonoids, 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.

Journal

Groups Complexity Cryptologyde Gruyter

Published: Nov 1, 2018

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