On the 𝑝-length and 𝔘-class of a 𝑝-solvable finite group

Abstract In finite group theory, 𝑝-length is an important invariant for a 𝑝-solvable group. The famous Hall–Higman 𝑝-length theorem states that the 𝑝-length of a 𝑝-solvable group is bounded by the nilpotent class of its Sylow 𝑝-subgroups. In this paper, we improve this result by giving a better estimate on the 𝑝-length of a 𝑝-solvable group in terms of the 𝔘-class of its Sylow 𝑝-subgroups.