Theoretical analysis demonstrates nilpotency in intersections of specific maximal subgroups in non-solvable groups, extending classical algebraic theorems.
In this paper, we prove that the intersection of all non-nilpotent maximal sub-groups of a non-solvable group containing the normalizer of some Sylow subgroup is nilpotent, which provides an extension of Shidov's theorem and Shlyk's theorem.
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Shi et al. (2026) studied this question.
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