Abstract
In this note, we show that if every maximal subgroup of a Sylow p-subgroup of a finite group has a p-solvable supplement then the group is necessarily p-solvable. This gives a positive answer to Problem 17.111 of the Kourovka Notebook (Unsolved Problems in Group Theory), which was posed by Skiba.
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Qian, G. Finite groups whose maximal subgroups of sylow p-subgroups admit a p-solvable supplement. Sci. China Math. 56, 1015–1018 (2013). https://doi.org/10.1007/s11425-012-4485-9
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DOI: https://doi.org/10.1007/s11425-012-4485-9