A subgroup H of G is said to be s-quasinormal in finite group G if H permutes with all Sylow subgroups of G.Let P be a Sylow p-subgroups of G.For these maximal subgroups of P that do not contain P ∩ Op(G),some new characterizations on p-nilpotent groups or p-supersolvable groups were obtained by utilizing their s-quasinormal properties,respectively.These results generalized existing theorems and provided an effective way to select maximal subgroups of Sylow p-subgroups.
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