Suzuki groups as expanders

TL;DR

This paper demonstrates that Suzuki groups can be generated to produce expander graphs, and by integrating prior research, it shows all non-abelian finite simple groups can be uniformly expanded.

Contribution

It introduces a method to select generators for Suzuki groups to form expanders and extends this to all non-abelian finite simple groups through existing deep results.

Findings

Suzuki groups can be generated to produce expanders

All non-abelian finite simple groups can be uniformly made into expanders

Connects group theory with expander graph constructions

Abstract

We show that pairs of generators for the family Sz(q) of Suzuki groups may be selected so that the corresponding Cayley graphs are expanders. By combining this with several deep works of Kassabov, Lubotzky and Nikolov, this establishes that the family of all non-abelian finite simple groups can be made into expanders in a uniform fashion.