The $\mathfrak F$-length of finite groups

L. A. Shemetkov [1] defined the concept of the $p$-length of an arbitrary finite group, generalizing the concept of the $p$-length of a $p$-solvable finite group of Hall–Higman [2]. In this article we introduce a more general concept of the $\mathfrak F$-length of an arbitrary finite group with respect to a certain formation $\mathfrak F$, and bounds on $\mathfrak F$-lengths and $p$-lengths are given for arbitrary finite groups.