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A distal property of groups and the growth of connected locally compact groups

Part of: Locally compact groups and their algebras

Published online by Cambridge University Press:  26 February 2010

Joseph Rosenblatt
Joseph Rosenblatt
Affiliation:
Mathematics Department, Ohio State University, Columbus, Ohio, 43210, U.S.A.
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Extract

If G is a topological group then we can think of G acting on itself by multiplying on the left. We would like to know when this action has the property that whenever g and h are distinct elements of G, then the element xg does not get arbitrarily close to xh as x varies in G. It is natural to say that this is the case if {(xg, xh): x∈G} is separated from the diagonal of G × G by a uniform neighbourhood of the diagonal.

MSC classification

Secondary: 22D05: General properties and structure of locally compact groups
Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979 , pp. 94 - 98
Copyright
Copyright © University College London 1979

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References

1.Abels, H.. “Distal affine transformation groups”, J. für reine u. ange. Math., 299–300 (1978), 293–300.Google Scholar
2.Helgason, S.. Differential geometry and symmetric spaces (Academic Press, New York, 1962).Google Scholar
3.Iwasawa, K.. “Some types of topological groups”, Annals of Math., 50 (1949), 507–558.CrossRefGoogle Scholar
4.Jenkins, J.. “Growth of connected locally compact groups”, J. of Functional Analysis, 12, 113–127 (1973).Google Scholar
5.Montgomery, D. and Zippin, L.. Topological transformation groups (Interscience Publishers, New York, 1955).Google Scholar
6.Moore, C. C.. “Distal affine transformation groups”, Amer. J. of Math., 90 (1968), 733–751.CrossRefGoogle Scholar