## Annals of Functional Analysis

### On a notion of closeness of groups

#### 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
Accepted: 2 January 2015
First available in Project Euclid: 15 October 2015

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

Digital Object Identifier
doi:10.1215/20088752-3163391

Mathematical Reviews number (MathSciNet)
MR3449337

Zentralblatt MATH identifier
1325.43004

#### 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

#### References

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