Abstract
Let G be a finite group. We say that a subgroup H of G is a CSS-subgroup in G, if there exists a normal subgroup K of G such that G = HK and H ∩ K is SS-quasinormal in G. In this paper, we study the p-nilpotency and supersolvability of G under the assumption that every member of a small subset of the set of all maximal subgroups of the Sylow p-subgroups P of G with certain property is a CSS-subgroup in G. Using this criterion, we obtain new results which generalize and unify recent results in the literature.
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