
doi: 10.1007/bf01142568
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 thef -length of an arbitrary finite group with respect to a certain formationf, and bounds onf-lengths and p-lengths are given for arbitrary finite groups.
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