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dc.contributor.authorAntolin, Yago
dc.contributor.authorMartino, Armando
dc.contributor.authorVentura Capell, Enric
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationAntolin, Y., Martino, A., Ventura, E. Degree of commutativity of infinite groups. "Proceedings of the American Mathematical Society", 16 Novembre 2016, vol. 145, núm. 2, p. 479-485.
dc.descriptionFirst published in Proceedings of the American Mathematical Society in volum 145, number 2, 2016, published by the American Mathematical Society
dc.description.abstractWe prove that, in a finitely generated residually finite group of subexponential growth, the proportion of commuting pairs is positive if and only if the group is virtually abelian. In particular, this covers the case where the group has polynomial growth (i.e., virtually nilpotent groups, where the hypothesis of residual finiteness is always satisfied). We also show that, for non-elementary hyperbolic groups, the proportion of commuting pairs is always zero.
dc.format.extent7 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject.lcshGroup theory
dc.subject.lcshAbelian groups
dc.subject.lcshInfinite groups
dc.subject.otherAbelian groups
dc.subject.otherDegree of commutativity
dc.subject.otherPolynomial growth
dc.titleDegree of commutativity of infinite groups
dc.subject.lemacGrups, Teoria de
dc.subject.lemacGrups abelians
dc.subject.lemacGrups infinits
dc.contributor.groupUniversitat Politècnica de Catalunya. MD - Matemàtica Discreta
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::20 Group theory and generalizations::20P05 Probabilistic methods in group theory
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
local.citation.authorAntolin, Y.; Martino, A.; Ventura, E.
local.citation.publicationNameProceedings of the American Mathematical Society

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