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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

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