Abstract
The main result of this paper states that if \({\mathcal {F}}\) is a subgroup-closed saturated formation of full characteristic, then the \({\mathcal {F}}\)-residual of a K-\({\mathcal {F}}\)-subnormal subgroup S of a finite group G is a large subgroup of G provided that the \({\mathcal {F}}\)-hypercentre of every subgroup X of G containing S is contained in the \({\mathcal {F}}\)-residual of X. This extends a recent result of Aivazidis, Safonova and Skiba.
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References
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Acknowledgements
This Project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under Grant no. (G: 789-130-1441). The authors, therefore, acknowledge with thanks DSR for technical and financial support.
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Al-Shomrani, M.M., Ballester-Bolinches, A. & Heliel, A.A. A Note on a Paper of Aivazidis, Safonova and Skiba. Mediterr. J. Math. 18, 213 (2021). https://doi.org/10.1007/s00009-021-01872-9
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DOI: https://doi.org/10.1007/s00009-021-01872-9