关于拟中心元的一个定理

A Theorem on Quasi-Central Element

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.