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.
作者
曾利江
ZENG Li-jiang(Northern Guizhou Istitute of Culture and Economy,Zunyi Normal College,Zunyi 563002,Guizhou,China)
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
关键词
有限群
超可解群
p-主因子
中心化子
正规子群
finite group
supersolvable group
p-main factors
centralizer
normal subgroup
作者简介
曾利江(1962-),男,贵州赤水人,教授。主要研究方向:代数学及其应用。
