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.
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)
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
basic mathematics
the theory of infinite groups
hereditary radical classes of groups
semisimple classes ofgroups
essential normal subgroup
