Let 𝐺 be a finite group.
An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of 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.
J. Lu is supported by the National Natural Science Foundation of China (11861015), Guangxi Natural Science Foundation Program (2019JJA110084), Guangxi Basic Ability Promotion Project for Young and Middle-aged Teachers (2020KY02019), the Training Program for 1,000 Young and Middle-aged Cadre Teachers in Universities of Guangxi Province.
W. Meng is supported by National Natural Science Foundation of China (11761079) and Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation.