有限群的m-正规子群

On M-Normal Subgroups in Finite Groups

定义了有限群的m -正规子群 ,并给出了下列结论 :1.若G的sylow子群全都是m -正规的 ,且至少有一个sylow子群在G中正规 ,则G可解 .2 .若G的sylow子群全都是m -正规的 ,且有一个sylow子群在G中正规 ,且 |G|至少有三个不同的素因子 ,则G幂零 .

with the concept of mnormal subgroups,this paper gives some result about msubgroups: 1.When all sylow subgroups about G is mnormal subgroups,and there is a sylow subgroups which is normal subgroup,finite group G is a solvable group. 2.When all sylow subgroups about G is mnormal subgroups,there is a sylow subgroups which is normal subgroup,and |G|=p α 1 1p α 2 2...p α n n,(n≥3),finite group G is a nilpotent group.