On a Generalized Centralizer Ring of a Finite Group Which Determines the Group

Abstract

The k-characters are class functions on subsets of Gk called the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of ℂGk, which we call the k-S-ring of G, and we think of these rings as generalized centralizer rings. We show that for a finite group G the 3-S-ring determines G. More specifically, the group characters and set products of certain 3-classes of G, which we call “uniform 3-classes”, determine G.