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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Lohrey, Markus


CiteScore 2018: 0.80

SCImago Journal Rank (SJR) 2018: 0.368
Source Normalized Impact per Paper (SNIP) 2018: 1.061

Mathematical Citation Quotient (MCQ) 2018: 0.38

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1869-6104
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On finitely generated submonoids of virtually free groups

Pedro V. Silva / Alexander Zakharov
Published Online: 2018-10-17 | DOI: https://doi.org/10.1515/gcc-2018-0008

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.

Keywords: Free group; virtually free group; submonoids; graded monoid; rational monoid; Kleene monoids; decidability

MSC 2010: 20E05; 20M05; 20F10; 68Q45; 68Q70

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About the article

Received: 2017-12-21

Published Online: 2018-10-17

Published in Print: 2018-11-01


Funding Source: Centro de Matemática Universidade do Porto

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

Funding Source: H2020 European Research Council

Award identifier / Grant number: 336983

Funding Source: Eusko Jaurlaritza

Award identifier / Grant number: IT974-16

Funding Source: Ministerio de Economía y Competitividad

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

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 15-01-05823

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).


Citation Information: Groups Complexity Cryptology, Volume 10, Issue 2, Pages 63–82, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2018-0008.

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