Geodesic
S-Subgroups of the Real Hyperbolic Groups
Canadian journal of mathematics, Tome 32 (1980) no. 1, pp. 246-256

Voir la notice de l'article provenant de la source Cambridge University Press

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]). 
O'Malley, Thomas J. S-Subgroups of the Real Hyperbolic Groups. Canadian journal of mathematics, Tome 32 (1980) no. 1, pp. 246-256. doi: 10.4153/CJM-1980-019-6
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