Subgroups of even Artin groups of FC-type
| dc.contributor.author | Antolín Pichel, Yago | |
| dc.contributor.author | Foniqi, Islam | |
| dc.date.accessioned | 2023-06-22T11:27:23Z | |
| dc.date.available | 2023-06-22T11:27:23Z | |
| dc.date.issued | 2023-05-26 | |
| dc.description.abstract | We prove a Tits alternative theorem for subgroups of finitely generated even Artin groups of FC type (EAFC groups), stating that there exists a finite index subgroup such that every subgroup of it is either finitely generated abelian, or maps onto a non-abelian free group. Parabolic subgroups play a key role, and we show that parabolic subgroups of EAFC groups are closed under taking roots. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación | |
| dc.description.sponsorship | Santander-UCM | |
| dc.description.status | unpub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/78891 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/72429 | |
| dc.language.iso | eng | |
| dc.relation.projectID | CEX2019-000904-S; PID2021-126254NB-I00 | |
| dc.relation.projectID | PR44/21-29907 | |
| dc.rights | Atribución 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by/3.0/es/ | |
| dc.subject.cdu | 512.54 | |
| dc.subject.keyword | Even Artin Groups | |
| dc.subject.keyword | FC type | |
| dc.subject.keyword | Parabolic subgroup | |
| dc.subject.keyword | Tits alternative | |
| dc.subject.keyword | Coherence | |
| dc.subject.ucm | Grupos (Matemáticas) | |
| dc.title | Subgroups of even Artin groups of FC-type | |
| dc.type | journal article | |
| dcterms.references | 1] Yago Antolín and Islam Foniqi. Intersection of parabolic subgroups in even Artin groups of FC-type. Proc. Edinb. Math. Soc. (2), 65(4):938–957, 2022. [2] Yago Antolín and Ashot Minasyan. Tits alternatives for graph products. Journal für die reine und angewandte Mathematik, 2015(704):55–83, 2015. [3] Gilbert Baumslag. A remark on generalized free products. Proc. Amer. Math. Soc., 13:53–54, 1962. [4] Rubén Blasco-García, Conchita Martínez-Pérez, and Luis Paris. Poly-freeness of even artin groups of fc type. Groups, Geometry, and Dynamics, 13(1):309–325, 2018. [5] J. O. Button. Tubular free by cyclic groups and the strongest tits alternative. arXiv math.GR 1510.05842, 2015. [6] Arjeh M. Cohen and David B. Wales. Linearity of Artin groups of finite type. Israel J. Math., 131:101–123, 2002. [7] Marc Culler and John W. Morgan. Group actions on R-trees. Proc. London Math. Soc. (3), 55(3):571–604, 1987. [8] María Cumplido, Volker Gebhardt, Juan González-Meneses, and Bert Wiest. On parabolic subgroups of Artin-Tits groups of spherical type. Adv. Math., 352:572–610, 2019. [9] María Cumplido, Alexandre Martin, and Nicolas Vaskou. Parabolic subgroups of large-type Artin groups. Math. Proc. Cambridge Philos. Soc., 174(2):393–414, 2023. [10] Warren Dicks and M. J. Dunwoody. Groups acting on graphs, volume 17 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1989. [11] Carl Droms. Graph groups, coherence, and three-manifolds. J. Algebra, 106(2):484–489, 1987. [12] Eddy Godelle. Parabolic subgroups of artin groups of type fc. Pacific journal of mathematics, 208(2):243–254, 2003. [13] CM Gordon. Artin groups, 3-manifolds and coherence. Bol. Soc. Mat. Mexicana, 10:193–198, 2004. [14] Thomas Haettel. Virtually cocompactly cubulated Artin-Tits groups. Int. Math. Res. Not. IMRN, (4):2919–2961, 2021. [15] Susan Hermiller and Zoran Šunić. Poly-free constructions for right-angled Artin groups. J. Group Theory, 10(1):117–138, 2007. [16] Susan M. Hermiller and John Meier. Artin groups, rewriting systems and three-manifolds. J. Pure Appl. Algebra, 136(2):141–156, 1999. [17] A. Karrass and D. Solitar. The subgroups of a free product of two groups with an amalgamated subgroup. Trans. Amer. Math. Soc., 150:227–255, 1970. [18] Daan Krammer. Braid groups are linear. Ann. of Math. (2), 155(1):131–156, 2002. [19] Gilbert Levitt. Generalized Baumslag–Solitar groups: rank and finite index subgroups. Annales de l’Institut Fourier, 65(2):725–762, 2015. [20] Alexandre Martin. The tits alternative for two-dimensional artin groups and wise’s power alternative. arXiv math.GR 2210.06369, 2022. [21] Alexandre Martin and Piotr Przytycki. Tits alternative for Artin groups of type FC. J. Group Theory, 23(4):563–573, 2020. [22] Alexandre Martin and Piotr Przytycki. Acylindrical actions for two-dimensional Artin groups of hyperbolic type. Int. Math. Res. Not. IMRN, (17):13099–13127, 2022. [23] Damian Osajda and Piotr Przytycki. Tits alternative for 2-dimensional CAT(0)-dimensional complexes. Forum Math. Pi, 10:Paper No. e25, 19, 2022. [24] Harm Van der Lek. The homotopy type of complex hyperplane complements. PhD thesis, Katholieke Universiteit te Nijmegen, 1983. [25] Daniel T. Wise. The last incoherent Artin group. Proc. Amer. Math. Soc., 141(1):139–149, 2013. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | bd3bab81-47d2-4551-811a-af8ac40597c5 | |
| relation.isAuthorOfPublication.latestForDiscovery | bd3bab81-47d2-4551-811a-af8ac40597c5 |
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