On the Characterization of Alternating 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 An be an alternating group of degree n ≥ 5. In this paper, we show that An is determined up to isomorphism by cod(An).