群为超可解群的另一个充要条件  

Another necessary and sufficient conditions about group is super solvable group

作　　者：曾利江[1] ZENG Lijiang(Northern Guizhou Institute of Culture and Economy,Zunyi Normal University,Zunyi 563000,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563000

出　　处：《安顺学院学报》2021年第3期121-124,共4页Journal of Anshun University

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。文章引进了前证明的一个定理,给出这个定理的一个推论作为本文备用,然后给出群的广义中心元的定义,并在此基础上进行研究,得到了几个引理,然后又给出了群的广义中心的定义,证明了关于它们的一些性质,最后用这些性质证明了一个充要条件:群G为超可解群当且仅当它和它的广义中心相等。Finite group theory has very important application in the natural sciences,the properties of the supersolvable group in group theory is extremely important.Article introduced a theorem proved many years ago,and a corollary of the theorem is given as a backup,this paper then gives the definition of generalized central element,and based on this study got a few lemma,then presents the definition of the generalized center of group,proved about some properties of about them,finally with these properties proved a necessary and sufficient condition:it is super solvable group if and only if it is equal to its generalized center.

关 键 词：有限群 超可解群 SYLOW子群 广义中心 循环子群 

分 类 号：O152[理学—数学]