Fusion systems provide an abstract framework for encoding the conjugacy relations of subgroups within a finite group, isolating the “p-local” behaviour at a fixed prime p. Rather than studying an ...

If G is a finite group, p is a prime, and P is a Sylow p-subgroup of G, we study how the exponent of the abelian group P/P′ is affected and how it affects the values of the complex characters of G.

The study of subgroups lies at the heart of finite group theory, exploring how smaller collections of elements interact within a larger algebraic system. Critical themes include normal subgroups, ...