Superstrong approximation
Superstrong approximation is a generalisation of strong approximation in algebraic groups to provide spectral gap results. A consequence of this property, holding for Zariski dense subgroups Γ of the special linear group over the integers, and in more general classes of algebraic groups G, is that the sequence of Cayley graphs for reductions Γp modulo prime numbers p, with respect to any fixed set S in Γ that is a symmetric set and generating set, is an expander family.[1][2]
Notes
- ^ Hee Oh; Emmanuel Breuillard (17 February 2014). Thin Groups and Superstrong Approximation. Cambridge University Press. p. x. ISBN 978-1-107-03685-7.
- ^ Hee Oh; Emmanuel Breuillard (17 February 2014). Thin Groups and Superstrong Approximation. Cambridge University Press. pp. 343–. ISBN 978-1-107-03685-7.