Let
G be a finite group and let
p be a prime such that (
p, |
G|) = 1. We study conditions under which the Abelian group
\Bbb F\Bbb F
p
[
G] has a few
G-orbits whose union generate it as an expander (equivalently, all the discrete Fourier coefficients (in absolute value) of this generating set are bounded away uniformly from one).
We prove a (nearly sharp) bound on the distribution of dimensions of irreducible representations of G which implies the existence of such expanding orbits. We further show a class of groups for which such a bound follows from the expansion properties of G. Together, these lead to a new iterative construction of expanding Cayley graphs of nearly constant degree.
Mathematics Subject Classification (2000):
05C25 - 20C15