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 (1H)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.

中文翻译：

---

𝒫-字符和有限可解基团的结构

令G为一个有限群。如果G是G的某个最大子集H的（1H）G {（1_ {H}）^ {G}}的不可约成分，则G的不可约字符称为𝒫{\ mathcal {P}}-字符。在本文中，我们以some {\ mathcal {P}}-个字符为条件，得出了可解基团G为p-幂零或p-封闭的一些条件。