Two results on character codegrees

Abstract

Let [Formula: see text] be a finite group and [Formula: see text] be the set of irreducible characters of [Formula: see text]. The codegree of an irreducible character [Formula: see text] of the group [Formula: see text] is defined as [Formula: see text]. In this paper, we study two topics related to the character codegrees. The first result is related to the prime graph of character codegrees and we show that the codegree prime graphs of several classes of groups can be characterized only by graph theoretical terms. The second result is about the [Formula: see text]-parts of the codegrees and character degrees.