Ballester-Bolinches, AdolfoCossey, JohnKamornikov, S. F.Meng, H.2018-01-090021-8693http://hdl.handle.net/1885/139099The 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 [10]. Our approach depends on results on regular orbits and it can be also used to extend a result of Mann [9] concerning intersections of injectors associated to Fitting classes.The first and fourth authors have been supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economía y Competitividad, Spain, and FEDER, European Union.application/pdf© 2017 Elsevier B.V.https://creativecommons.org/licenses/by-nc-nd/4.0/Finite groupsSoluble groupsFormationsFitting classesPrefrattini subgroupsNormalisersInjectors201710.1016/j.jalgebra.2017.12.014Creative Commons Attribution Non-Commercial No Derivatives License