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Problems related to the Lockett Conjecture on Fitting classes of finite groups |
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| Authors: | Wenbin Guo |
| Affiliation: | a Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, P.R. China b Department of Mathematics, Hong Kong University, Pokfulam Road, Hong Kong, PR. China (SAR) c Department of Mathematics, Vitebsk State University, Vitebsk 210038, Belarus |
| Abstract: | The existence of a solvable non-normal Fitting class F which is not a Lockett class but for which the Lockett Conjecture still holds are studied. We also prove that there exists an ω-local Fitting class F which does not satisfy the Lockett conjecture but the Lockett conjecture still holds under a given condition. As a consequence of our result, a generalized version of the Lausch's problem in the well-known Kourovka Notebook is answered. |
| Keywords: | 20D10 |
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