Annals of Functional Analysis

On a notion of closeness of groups

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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1444913696

Digital Object Identifier
doi:10.1215/20088752-3163391

Mathematical Reviews number (MathSciNet)
MR3449337

Zentralblatt MATH identifier
1325.43004

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

Keywords
discrete groups group representations distance between groups

Citation

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. https://projecteuclid.org/euclid.afa/1444913696


Export citation

References

  • [1] E. Christensen, A. M. Sinclair, R. R. Smith, S. A. White, and W. Winter, Perturbation of nuclear $C^{*}$-algebras, Acta Math. 208 (2012), no. 1, 93–150.
  • [2] R. V. Kadison and D. Kastler, Perturbations of von Neumann algebras, I: Stability of type, Amer. J. Math. 94 (1972), 38–54.
  • [3] W. J. Shi, A characteristic property of $\mathrm{PSL}_{2}(7)$, J. Austral. Math. Soc. Ser. A 36 (1984), no. 3, 354–356.