关于拟中心元的一个定理  

A Theorem on Quasi-Central Element

作　　者：曾利江[1] ZENG Lijiang(Northern Guizhou Institute of Culture and Economy, Zunyi Normal University, Zunyi,GuiZhou 563000,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：《内江师范学院学报》2020年第6期59-62,共4页Journal of Neijiang Normal University

摘　　要：引进了一些记号,并用这些记号研究了可解群的一个性质,对群的中心元这一概念进行了拓广,得到拟中心元的概念,证明了关于拟中心元的一些性质,利用这些性质证明了关于拟中心元的一个定理,即:设群G的拟中心元x的阶为素数p,则或者x∈Z*(G)或者〈x〉■G.Some notations are introduced and one of the properties for a solvable group is proved by use of these notations,and the concept of central element was generalized into the concept of quasi-central element,and some properties on quasi-central elements are proven.Based on these properties,a theorem on quasi-central element is proved,i.e.Given that the order for the quasi-central element x of group G is a prime number p,then x∈Z*(G)or〈x〉■G must be true.

关 键 词：拟中心元 广义中心元 SYLOW P-子群 极大子群 正规子群 

分 类 号：O152[理学—数学]