Thin group (algebraic group theory)
In algebraic group theory, a thin group is a discrete Zariski-dense subgroup of G that has infinite covolume, where G is a semisimple algebraic group over the reals. This is in contrast to a lattice, which is a discrete subgroup of finite covolume.
The theory of "group expansion" for particular thin groups has been applied to arithmetic properties of Apollonian circles and in Zaremba's conjecture.
