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Thef-length of finite groups

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Abstract

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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Translated from Matematicheskii Zametki, Vol. 19, No. 5, pp. 745–754, May, 1976.

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Kharlamova, V.I. Thef-length of finite groups. Mathematical Notes of the Academy of Sciences of the USSR 19, 442–447 (1976). https://doi.org/10.1007/BF01142568

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Keywords

  • Finite Group
  • General Concept
  • Arbitrary Finite Group