On the Characterization of Sporadic Simple Groups by Codegrees

Abstract

Let G be a finite group and Irr(G) the set of all irreducible complex characters of G. Define the codegree of χ ∈ Irr(G) as cod(χ) :=and denote by cod(G) := {cod(χ)|χ ∈ Irr(G)} the codegree set of G. Let H be one of the 26 sporadic simple groups. In this paper, we show that H is determined up to isomorphism by cod(H).