Ultraproducts of Quasirandom Groups

What is it about?

The author explored some structures about how conjugacy classes of elements could cover a non-abelian finite simple group, i.e., the covering properties. Using these facts, the author established and generalized some representation properties of ultraproducts of non-abelian finite simple groups, and groups that are close enough to them.

Featured Image

Why is it important?

The covering properties is essentially a way to compare the "shapes" of non-abelian finite simple groups with shapes of compact Lie groups, so it is a useful tool. Also, understanding ultraproducts of finite groups can help with understanding "Ramsey-type" results on finite groups, and can give rise to some interesting examples in topological group theory.