Expansion of coset graphs of PSL2(Fp)
Abstract
Let G be a finite group and let H1,H2<G be two subgroups. In this paper, we are concerned with the bipartite graph whose vertices are G/H1 G/H2 and a coset g1H1 is connected with another coset g2H2 if and only if g1H1 g2 H2≠. The main result of the paper establishes the existence of such graphs with large girth and large spectral gap. Lubotzky, Manning and Wilton use such graphs to construct certain infinite groups of interest in geometric group theory.
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