Abstract
Let G G be a finite group, and p p a prime number; a character of G G is called p p -constant if it takes a constant value on all the elements of G G whose order is divisible by p p . This is a generalization of the very important concept of characters of p p -defect zero. In this paper, we characterize the finite p p -solvable groups having a faithful irreducible character that is p p -constant and not of p p -defect zero, and we will show that a non- p p -solvable group with this property is an almost-simple group.
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