
doi: 10.2307/2373310
Introduction. This paper is inspired by Kazhdan's work [8]. In [8], he has studied the structure of lattices, i.e., discrete subgroups with finite invariant measure on the factor space, of a Lie group by investigating a particular topological property of the dual space of a Lie group. Let G be a separable locally compact group and G its dual space. G is said to have property (T) if the class of the trivial representation2 is an isolated point in G. In [8], it is proved that if G has property (T), then any lattice P of G also has property (T) ; in particular, by [8, Theorem 2], P is finitely generated and r/[Jr, r] is finite. Kazhdan has proved that connected simple Lie groups with finite center and R-rank > 2 have property (T) based on his study of SL(3,R). Here by the same approach, we show that SO(2,3) has property (T). Thus we are able to conclude the following theorem:
group theory
group theory
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