On c-normal maximal and minimal subgroups of Sylow p-subgroups of finite groups

A subgroup H of a finite groupG is called c-normal inG if there exists a normal subgroupN of G such thatG = HN and $H cap N leq H_{G} = {rm core}_{G}(H)$. In this paper, we investigate the class of groupsof which every maximal subgroup of its Sylowp-subgroup is c-normal and theclass of groups of which some minimal subgroups of its Sylowp-subgroup is c-normal for some prime numberp. Some interesting results are obtained andconsequently, many known results related top-nilpotent groups andp-supersolvable groups are generalized.