Presentations of generalisations of Thompson's Group V

Martínez-Pérez, Conchita (Universidad de Zaragoza) ; Matucci, Francesco ; Nucinkis, Brita

Resumen: We consider generalisations of Thompson''s group V, denoted by Vr(S), which also include the groups of Higman, Stein and Brin. We showed earlier (Forum Math. 28:5 (2016), 909-921) that under some mild conditions these groups and centralisers of their finite subgroups are of type F8. Under more general conditions we show that the groups Vr(S) are finitely generated and, under the mild conditions mentioned above for which they are of type F8 and hence finitely presented, we give a recipe to find explicit presentations. For the centralisers of finite subgroups we find a suitable infinite presentation and then show how to apply a general procedure to shorten this presentation. In the appendix, we give a proof of this general shortening procedure.

Idioma: Inglés

DOI: 10.2140/pjm.2018.296.371

Año: 2018

Publicado en: PACIFIC JOURNAL OF MATHEMATICS 296, 2 (2018), 371-403
ISSN: 0030-8730

Factor impacto JCR: 0.576 (2018)

Categ. JCR: MATHEMATICS rank: 224 / 313 = 0.716 (2018) - Q3 - T3

Factor impacto SCIMAGO: 1.03 - Mathematics (miscellaneous) (Q1)

Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-67781-P

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Algebra (Dpto. Matemáticas)