Carter subgroups and Fitting heights of finite groups |
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Authors: | Wenbin Guo E P Vdovin |
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Institution: | 1.Department of Mathematics,University of Science and Technology of China,Hefei,People’s Republic of China;2.Sobolev Institute of Mathematics and Novosibirsk State University,Novosibirsk,Russia |
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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. |
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