Equivalent version of Huppert's conjecture on the codegrees

TL;DR

This paper proves that the simple group PSL(2, q) for q > 3 is uniquely identified by its set of codegrees, extending the understanding of group characterization via character theory.

Contribution

It establishes that PSL(2, q) can be uniquely determined by its codegree set, providing a new perspective on group recognition through character codegrees.

Findings

PSL(2, q) is uniquely determined by its codegree set for q > 3

The codegree set characterizes the simple group uniquely

Extends the scope of Huppert's conjecture to codegrees

Abstract

Let G be a finite group, Irr(G) the set of all irreducible complex characters of G and X \in Irr(G). Let also cod(X) = |G : kerX|/X(1) and cod(G) = {cod(X) | X \in Irr(G)}. In this note, we show that the simple group PSL(2, q), for a prime power q > 3, is uniquely determined by the set of its codegree.