𝒫-characters and the structure of finite solvable groups

Abstract

Abstract Let G be a finite group. An irreducible character of G is called a 𝒫 {\mathcal{P}} -character if it is an irreducible constituent of ( 1 H ) G {(1_{H})^{G}} for some maximal subgroup H of G. In this paper, we obtain some conditions for a solvable group G to be p-nilpotent or p-closed in terms of 𝒫 {\mathcal{P}} -characters.