关于可解群是超可解群的一个结论

Some conclusion about solvable group is supersolvable group

有限群的性质是极其丰富的,它在各个自然科学中起到了极其重要的作用。首先给出拟正规子群的定义,对这个定义作深入的研究,得到几个引理,然后给出了2-极大子群的定义,用前面已经证明的几个引理,并借助次正规子群的性质,证明当2-极大子群均为拟正规时,群G是超可解的,当群G的阶的素因子个数不小于3时,群G还是幂零的。

The properties of finite group is extremely rich,in various natural sciences it played an extremely important role。First the definition of is presented,and this definition is researched in deep level,got a few lemma,then gives the definition of 2-great subgroup,base on several lemma has been proved,and with the aid of the properties of subnormal subgroup,proved when 2-great subgroup are quasi-normal,the solvability of group G is supersolvable,and when a the number of prime divisor of group G’s order is not less than 3,G is nilpotent group.