Regular left-orders on groups
| dc.contributor.author | Antolín Pichel, Yago | |
| dc.contributor.author | Rivas, Cristóbal | |
| dc.contributor.author | Lu Su, Hang | |
| dc.date.accessioned | 2023-06-17T08:28:10Z | |
| dc.date.available | 2023-06-17T08:28:10Z | |
| dc.date.issued | 2021-04-12 | |
| dc.description.abstract | A regular left-order on finitely generated group a group G is a total, left-multiplication invariant order on G whose corresponding positive cone is the image of a regular language over the generating set of the group under the evaluation map. We show that admitting regular left-orders is stable under extensions and wreath products and give a classification of the groups all whose left-orders are regular left-orders. In addition, we prove that solvable Baumslag-Solitar groups B(1, n) admits a regular left-order if and only if n ≥ −1. Finally, Hermiller and Sunic showed that no free product admits a regular left-order, however we show that if A and B are groups with regular left-orders, then (A ∗ B) × Z admits a regular left-order. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.sponsorship | Unión Europea. Horizonte 2020 | |
| dc.description.sponsorship | Ministerio de Economía y Competitividad (MINECO) | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
| dc.description.sponsorship | Centro de Excelencia Severo Ochoa | |
| dc.description.sponsorship | Fundación "La Caixa" | |
| dc.description.sponsorship | Gobierno de Chile | |
| dc.description.status | unpub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/72936 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/7213 | |
| dc.language.iso | eng | |
| dc.relation.projectID | INPhINIT (713673) | |
| dc.relation.projectID | MTM2017-82690-P | |
| dc.relation.projectID | CEX2019-000904-S | |
| dc.relation.projectID | SEV-2015-0554 | |
| dc.relation.projectID | LCF/BQ/IN17/11620066 | |
| dc.relation.projectID | Fondecyt (1181548); Fondecyt (1210155) | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512.54 | |
| dc.subject.keyword | Ordered groups | |
| dc.subject.keyword | Formal languages | |
| dc.subject.keyword | Baumslag-Solitar groups | |
| dc.subject.ucm | Cibernética matemática | |
| dc.subject.ucm | Grupos (Matemáticas) | |
| dc.subject.unesco | 1207.03 Cibernética | |
| dc.title | Regular left-orders on groups | |
| dc.type | journal article | |
| dcterms.references | [1] J. Alonso, Y. Antolin, J. Brum, C. Rivas, On the geometry of positive cones, Preprint (2020) [2] A.V. Anisimov. The group languages. Kibernetika (Kiev) 1971, no. 4, 18–24. [3] Y. Antolín, W. Dicks, Z. Sunic, Left relativity convex subgroups. Topological methods in group theory, 1–18, London Math. Soc. Lecture Note Ser., 451, Cambridge Univ. Press, Cambridge, 2018. [4] J. Berstel, Transductions and context-free languages. Leitfäden der Angewandten Mathematik und Mechanik [Guides to Applied Mathematics and Mechanics], 38. B. G. Teubner, Stuttgart, 1979. [5] C. Bleak, F. Matucci, M. Neunhöffer, Embeddings into Thompson’s group V and coCF groups. J. Lond. Math. Soc. (2) 94 (2016), no. 2, 583–597. [6] C. Bonatti, I. Monteverde, A. Navas, C. Rivas, Rigidity for C 1-actions on the interval arising from hyperbolicity I: solvable groups. Math. Z. (2017) 286:919–949. [7] R. Bieri, W. D. Neumann, and R. Strebel. A geometric invariant of discrete groups. Invent. Math. 90 (1987), 451–477. [8] D. Calegari. Problems in foliations and laminations of 3-manifolds. In Topology and geometry of manifolds (Athens, GA, 2001), volume 71 of Proc.Sympos. Pure Math., pages 297–335. Amer. Math. Soc., Providence, RI, 2003. [9] N. Chomsky, . Three models for the description of language, IRE Transactions on Information Theory (2): 113–124(1956)39 [10] Arman Darbinyan, Computability, orders, and solvable groups. Jounal of Symbolic Logic (to appear) [11] W. Dicks, and Z. Sunic, Orders on trees and free products of left-ordered groups. Canad. Math. Bull. 63 (2020), no. 2, 335–347 [12] C. Droms. Subgroups of Graphs Groups, Journal of Algebra, 110 (2) (1987),519–522. [13] B. Deroin, A. Navas, C. Rivas. Groups, Orders, and Dynamics. Preprint (2016), available on arXiv:1408.5805v2. [14] M. Harrison-Trainor, Left-orderable computable groups. J. Symbolic Logic 83 (2018), no. 1, 237–255. [15] S. Hermiller, J. Meier. Artin groups, rewriting systems and three-manifolds. J. Pure Appl. Algebra 136 (1999), no. 2, 141–156. [16] S. Hermiller, Z. Sunic. No positive cone in a free product is regular, Internat. J. Algebra Comput. 27 (2017), 1113-1120. [17] D. F. Holt, Sarah Rees, Claas E. Röver, and Richard M. Thomas. Groups with contextfree co-word problem. J. London Math. Soc. (2), 71(3):643–657, 2005 [18] J. Hopcroft, R. Motwani and J. D. Ullman. Introduction to Automata Theory, Languages and Computation, Reading, MA: Addison-Wesley. 3rd Edition (2006). [19] V. M. Kopytov, N. Y. Medv.edev Right-ordered groups, Consultants Bureau, New York, Siberian School of Algebra and Logic (1996). [20] J. Lehnert, P. Schweitzer. The co-word problem for the Higman-Thompson group is context-free, Bull. Lond. Math. Soc. 39 (2007), no. 2, 235–241. [21] G. Levitt, Quotients and subgroups of Baumslag-Solitar groups. Journal of Group Theory 18.1 (2015): 1–43. [22] P. Linnell. The space of left-orders of a group is either finite or uncountable. Bull. London Math. Society 43 (2011), no. 1, 200–202. [23] D. W. Morris. Amenable groups that act on the line. Algebraic & Geometric Topology 6 (2006), 2509–2518. [24] D. E. Muller, P. E. Schupp, Groups, the theory of ends, and context-free languages, J. computer and system science. 26 (1983), 295–310. [25] D. S. Passman. The algebraic structure of group rings. Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. [26] Edited by G. Rozenberg and A. Salomaa. Handbook of formal languages. Vol. 1. Word, language, grammar. Springer-Verlag, Berlin, 1997. xxiv+873 pp. 40 [27] C. Rivas. On the space of Conradian group orderings. J. of Group Theory, 13 (2010), 337–353. [28] C. Rourke, B. Wiest. Order automatic mapping class groups. Pacific J. Math. 194 (2000), no. 1, 209–227. [29] D. Segal. Polycyclic groups. Cambridge Tracts in Mathematics, 82. Cambridge University Press,1983. [30] H.L. Su. Formal language convexity in left-orderable groups. Internat. J. Algebra Comput. Vol. 30, No. 07, pp. 1437–1456 (2020) [31] Z. Sunic. Explicit left orders on free groups extending the lexicographic order on free monoids. C. R. Math. Acad. Sci. Paris 351 (2013), no. 13-14, 507–511. [32] Z. Sunic. Orders on free groups induced by oriented words. Available at http://arxiv.org/abs/1309.6070, 2013 [33] V. Tararin. On groups having a finite number of orders. Dep. Viniti (Report), Moscow(1991). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | bd3bab81-47d2-4551-811a-af8ac40597c5 | |
| relation.isAuthorOfPublication.latestForDiscovery | bd3bab81-47d2-4551-811a-af8ac40597c5 |
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