Archiv der Mathematik

, Volume 110, Issue 5, pp 427–432 | Cite as

Carter subgroups and Fitting heights of finite groups

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Abstract

Let G be a finite group possessing a Carter subgroup K. Denote by \(\mathbf {h}(G)\) the Fitting height of G, by \(\mathbf {h}^*(G)\) the generalized Fitting height of G, and by \(\ell (K)\) the number of composition factors of K, that is, the number of prime divisors of the order of K with multiplicities. In 1969, E. C. Dade proved that if G is solvable, then \(\mathbf {h}(G)\) is bounded in terms of \(\ell (K)\). In this paper, we show that \(\mathbf {h}^*(G)\) is bounded in terms of \(\ell (K)\) as well.

Keywords

Finite group Carter subgroup Generalized Fitting subgroup Generalized Fitting height 

Mathematics Subject Classification

20D25 20D30 

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Notes

Acknowledgements

The authors express gratitude to Professor E.I.Khukhro for his comments and suggestions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  2. 2.Sobolev Institute of Mathematics and Novosibirsk State UniversityNovosibirskRussia

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