一类无限群中局部幂零性的判定准则  

A CRITERION FOR LOCAL NILPOTENCE IN A CLASS OF INFINITE GROUPS

作　　者：张志让[1] 

机构地区：[1]成都信息工程学院,成都610041

出　　处：《数学年刊（A辑）》2004年第2期165-170,共6页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19771013);四川省应用基础研究(No.03JY029-020)资助的项目.

摘　　要：设G是任意群,群G的Frattini子群nat(G)定义为G的所有极大子群的交.类似地,群G的另外两个特征子群nFrat(G)及R(G)分别定义为群G的所有极大正规子群及群G的所有正规的极大子群的交.本文通过对nat(G),nnat(G)及R(G)的相互包含关系的研究,得到CF-群或中心由多重循环群的扩张群中局部幂零性的一个判定准则.同时也讨论了在某些群类中若干种广义幂零性的等价性.For any group G, the Frattini subgroup Frat(G) is the intersection of the maximal subgroups of G. In this article a criterion for local nilpotence of central-by- (finite or polycyclic) groups is established by the investigation of mutual containments of Frat(G) and two other Frattini-like subgroups, nFrat(G) and -R(G) which are denned as the intersections of the maximal normal subgroups and normal maximal subgroups, respectively. Also equivalences of generalized nilpotences are discussed in some classes of groups.

关 键 词：FC-群 CF-群 中心由多重循环群的扩张群 局部幂零性 超限下中心性 FRATTINI子群 

分 类 号：O152.1[理学—数学]