Semi Cover-avoidance Properties And The Structure Of Finite Groups

It is an important method to study the structures of finite groups by the subgroups. In this paper, we proved that some results about the c— normal subgroups can still hold when we replace the conditions by semi cover-avoiding groups, and obtain some new results. The main results are the following:(1) We give some results on solvablity of finite groups by the semi-CAP property of some maximal subgroups and generalize some conclusions on c— normality.(2) We give some results on solvability and supersolvablity of finite groups by the semi-CAP property of some Hall subgroups, Sylow subgroups and some maximal subgroups of Sylow subgroups.(3) We give some results on supersolvablity and p— nilpotency of finite groups by the semi-CAP property of some minimal subgroups and generalize some results on CAP subgroups and c— normal subgroups.