关于子群均素数阶的群为超可解群的一个判定结论  

A decision conclusion about group which subgroup all be prime order be Supersolvable group

作　　者：曾利江[1] ZENG Li-jiang(Northern Guizhou Istitute of Culture and Economy,Zunyi Normal College,Zunyi 563002,Guizhou,China)

机构地区：[1]遵义师范学院黔北文化与经济研究院,贵州遵义563002

出　　处：《贵阳学院学报（自然科学版）》2020年第4期1-5,共5页Journal of Guiyang University：Natural Sciences

摘　　要：有限群理论在自然科学中有着极其重要的应用,有限群中超可解群的性质极其重要,通过定义了主因子,p-主因子及群的中心化子等概念,对这些概念进行深入的研究,得到一系列引理,最后利用这些引理证明了在群G是奇数阶的情况下,如果G中凡素数阶的子群都是正规的,则G是超可解群这一重要的判定结论。Theory of finite group has a very important application in natural science,it is extremely important that the properties of the supersolvable group.This paper first defines the main factor,p-main factors and the group of centralizer and other concepts.And then research in-depth to these concepts,and get a series of lemma.The use of the lemmas is proved under the condition of the group G is an odd number of order,if every prime order subgroup of G is normal,then G is supersolvable group.Obviously,this is an important decision conclusion.

关 键 词：有限群 超可解群 p-主因子 中心化子 正规子群 

分 类 号：O152[理学—数学]