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February 2016 On a notion of closeness of groups
Chi-Wai Leung, Chi-Keung Ng, Ngai-Ching Wong
Ann. Funct. Anal. 7(1): 24-32 (February 2016). DOI: 10.1215/20088752-3163391


Enlightened by the notion of perturbation of C-algebras, we introduce, and study briefly in this article, a notion of closeness of groups. We show that if two groups are “close enough” to each other, and one of them has the property that the orders of its elements have a uniform finite upper bound, then these two groups are isomorphic (but in general they are not). We also study groups that are close to abelian groups, as well as an equivalence relation induced by closeness.


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Chi-Wai Leung. Chi-Keung Ng. Ngai-Ching Wong. "On a notion of closeness of groups." Ann. Funct. Anal. 7 (1) 24 - 32, February 2016.


Received: 21 November 2014; Accepted: 2 January 2015; Published: February 2016
First available in Project Euclid: 15 October 2015

zbMATH: 1325.43004
MathSciNet: MR3449337
Digital Object Identifier: 10.1215/20088752-3163391

Primary: ‎43A65
Secondary: 43A20

Keywords: discrete groups , distance between groups , group representations

Rights: Copyright © 2016 Tusi Mathematical Research Group


Vol.7 • No. 1 • February 2016
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