遗传根群类和半单群类  

Hereditary Radical Classes and Semisimple Classes of Groups

作　　者：陈生生[1] 张志让[1] 

机构地区：[1]成都信息工程学院数学学院,四川成都610225

出　　处：《成都信息工程学院学报》2012年第5期507-510,共4页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(11071229)

摘　　要：针对Li X.M分别给出的根群类和半单群类的若干特征性质,提出了根群类和半单群类之间应具有的联系。通过群的一类特殊的正规子群:本质正规子群将根群类和半单群类联系起来,并利用群的根性的一般理论,得到了两个结果:根群类P是遗传的当且仅当其对应的半单群类L是本质扩张闭的;当根群类P是遗传根群类时,根群类P和其对应的半单群类L所决定的群类M是根群类。Based on several characterizations of radical classes and semisimple classes of groups given respectively by Li X M, the relationship of radical classes and semisimple classes of groups is proposed. Linked to radical classes of groups and semisimple classes of groups by a special normal subgroup of a group, the essential normal subgroup, and by using the general theory of radical properties of groups, we got the following two results. A radical class P of groups is hereditary if and only if the corresponding semisimple class L of groups is closed under essential extension. If a radical class P is a hereditary radical class of groups, then the class M of groups determined by P and the corre- sponding semisimple class L is a radical class of groups.

关 键 词：基础数学 无限群论 遗传根群类 半单群类 本质正规子群 

分 类 号：O152.7[理学—数学]