On finite groups with certain maximal CSS-subgroups.

AbstractLet 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. [ABSTRACT FROM AUTHOR]