Expansion of coset graphs of PSL_2(F_p)

Péter P. Varjú

doi:10.1007/s11856-019-1907-1

paper

Expansion of coset graphs of PSL_2(F_p)

arXiv:1810.09925 · doi:10.1007/s11856-019-1907-1

Abstract

Let $G$ be a finite group and let $H_{1}, H_{2} < G$ be two subgroups. In this paper, we are concerned with the bipartite graph whose vertices are $G / H_{1} \cup G / H_{2}$ and a coset $g_{1} H_{1}$ is connected with another coset $g_{2} H_{2}$ if and only if $g_{1} H_{1} \cap g_{2} H_{2} \neq = \emptyset$ . 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.

13 pages; version accepted for publication in Israel J. Math.; minor corrections based on referee's report; results and proofs are unchanged

References in corpus (1)

On the girth of random Cayley graphs