A sufficient and necessary condition for p-nilpotence of a finite group.

In this paper, we introduce a condition on a p-subgroup of a finite group that is more general than the concept of ICΦ-subgroups, and obtain a sufficient and necessary condition for p-nilpotence of a finite group. We not only simplify the proofs of some main theorems of Gao and Li [<italic>Acta Math. Hungar.</italic> <bold>163</bold>(1) (2021) 29–36], Kaspczyk [<italic>Acta Math. Hungar.</italic> <bold>165</bold>(2) (2021) 355–359], and Kaspczyk [<italic>J. Algebra Appl.</italic> <bold>23</bold>(1) (2024) 2450016], but also generalize these results. [ABSTRACT FROM AUTHOR]