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S-Subgroups of the Real Hyperbolic Groups

Published online by Cambridge University Press:  20 November 2018

Thomas J. O'Malley
Thomas J. O'Malley*
Affiliation:
Le Moyne College, Syracuse, New York
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If H is a closed subgroup of a locally compact group G, with G/H having finite G-invariant measure, then, as observed by Atle Selberg [8], for any neighborhood U of the identity in G and any element g in G, there is an integer n > 0 such that gn is in U·H·U. A subgroup satisfying this latter condition is said to be an S-sub group, or satisfies property (S). If G is a solvable Lie group, then the converse of Selberg's result has been proved by S. P. Wang [10]: If H is a closed S-subgroup of G, then G/H is compact. Property (S) has been used by A. Borel in the important “density theorem” (see Section 2 or [1]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 1 , 01 February 1980 , pp. 246 - 256
Copyright
Copyright © Canadian Mathematical Society 1980

References

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