Abstract
Let \(\mathfrak {F}\) be a subgroup-closed saturated formation of finite groups containing all finite nilpotent groups, and let M be a subgroup of a finite group G normalising the \(\mathfrak {F}\)-residual of every non-subnormal subgroup of G. We show that M normalises the \(\mathfrak {F}\)-residual of every subgroup of G. This answers a question posed by Gong and Isaacs (Arch Math 108:1–7, 2017) when \(\mathfrak {F}\) is the formation of all finite supersoluble groups.
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References
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Ballester-Bolinches, A., Kamornikov, S.F. & Meng, H. Normalisers of residuals of finite groups. Arch. Math. 109, 305–310 (2017). https://doi.org/10.1007/s00013-017-1074-8
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DOI: https://doi.org/10.1007/s00013-017-1074-8