Annals of Functional Analysis

On a notion of closeness of groups

Chi-Wai Leung, Chi-Keung Ng, and Ngai-Ching Wong

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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.

Article information

Ann. Funct. Anal., Volume 7, Number 1 (2016), 24-32.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 43A65: Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]
Secondary: 43A20: $L^1$-algebras on groups, semigroups, etc.

discrete groups group representations distance between groups


Leung, Chi-Wai; Ng, Chi-Keung; Wong, Ngai-Ching. On a notion of closeness of groups. Ann. Funct. Anal. 7 (2016), no. 1, 24--32. doi:10.1215/20088752-3163391.

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