𝒫-characters and the structure of finite solvable groups

Abstract

Let 𝐺 be a finite group. An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of (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-characters.

Normal $p$-complements and irreducible character codegrees

“…Following [9], we call χ a P-character of G with respect to H, and denote by Irr P (G) the set of P-characters of G. In [9], Qian and Yang showed many interesting facts about P-characters in a finite solvable group. Lu, Wu and Meng [7] proved that if G is a p-solvable group and cod(χ) is a p ′ -number for every χ ∈ Irr P (G), then G is p-nilpotent.…”