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Title:
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Degree of commutativity of infinite groups
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Author:
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Antolin, Yago; Martino, Armando; Ventura Capell, Enric
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta |
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Abstract:
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First published in Proceedings of the American Mathematical Society in volum 145, number 2, 2016, published by the American Mathematical Society |
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Abstract:
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We 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. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
-Group theory
-Abelian groups
-Infinite groups
-Abelian groups
-Degree of commutativity
-Polynomial growth
-Grups, Teoria de
-Grups abelians
-Grups infinits
-Classificació AMS::20 Group theory and generalizations::20P05 Probabilistic methods in group theory |
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Rights:
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Document type:
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Article - Submitted version
Article |
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