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A. Ballester-Bolinches, John Cossey, S. F. Kamornikov, H. Meng.
On two questions from the Kourovka Notebook
J. Algebra, 499:438-449, 2018
The aim of this paper is to give answers to some questions concerning intersections of system normalisers and prefrattini subgroups of finite soluble groups raised by the third author, Shemetkov and Vasil’ev in the Kourovka Notebook . Our approach depends on results on regular orbits and it can be also used to extend a result of Mann  concerning intersections of injectors associated to Fitting classes.
2010 Mathematics Subject Classification: 20D10, 20D20
Keywords: Finite groups. Soluble groups. Formations. Fitting classes. Prefrattini subgroups. Normalisers. Injectors.