On weak m-normal subgroups in finite group

With the concept of weak m-normal subgroups,some results about weak m-normal subgroups are given:(1)When all Sylow subgroups about G are weak m-normal subgroups,and there is a Sylow subgroup which is normal subgroup of M,M is a maximal subgroup of G,then M is a solvable group.(2)When all Sylow subgroups about G are weak m-normal subgroups,and there is no any Sylow subgroup which is normal subgroup of M,M is a maximal subgroup of G,then M is not a solvable group.(3)Let G be a finite group,and M is a maximal subgroup of G,all Sylow subgroups about G are weak m-normal subgroups,then M is a solvable group if and only if there is a Sylow subgroup which is normal subgroup of M.(4)When all Sylow subgroups about G are weak m-normal subgroups,and there is a Sylow subgroup which is normal subgroup of of M,M is a maximal subgroup of G,and|M|=Pa11Pa22…Pann(n≥3),then finite group G is a solvable group.(5)When M is a maximal subgroup of G,and M is a solvable group,all Sylow subgroups about M are not cyclic groups,and they are weak m-normal subgroups of G,then finite group G is a solvable group.