Super-π-Brauer Characters and Super-π-Regular Classes

Abstract

Supercharacter theories for an arbitrary finite group were developed by Diaconis and Isaacs. Let G* denote the set of all π-regular elements of G. Set Iπ(G) = {χ* | χ ∈Irr(G) and χ* ≠ α* + β* for characters α, β of G}, where χ* means the restriction of χ to G*. In this paper, we consider the partitions of Iπ(G) and G* for a π-separable group G. We obtain some results which generalize those of Diaconis and Isaacs.