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On finitely generated submonoids of virtually free groups

  • Pedro V. Silva EMAIL logo and Alexander Zakharov

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 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.

Award Identifier / Grant number: UID/MAT/00144/2013

Award Identifier / Grant number: 336983

Funding source: Eusko Jaurlaritza

Award Identifier / Grant number: IT974-16

Award Identifier / Grant number: MTM2014-53810-C2-2-P

Award Identifier / Grant number: 15-01-05823

Funding statement: Both authors were partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds (FEDER), under the partnership agreement PT2020. The second author was also partially supported by the ERC Grant 336983, by the Basque Government grant IT974-16, by the grant MTM2014-53810-C2-2-P of the Ministerio de Economía y Competitividad of Spain, and by the Russian Foundation for Basic Research (project no. 15-01-05823).

Acknowledgements

We are grateful to the referees for insightful comments and suggestions which have improved the paper.

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Received: 2017-12-21
Published Online: 2018-10-17
Published in Print: 2018-11-01

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