群的融合自由积的fnFrattini子群和fcFrattini子群

邓理平;邢世奇;张志让

【期刊名称】《成都信息工程学院学报》

【年(卷),期】2011(026)003

【摘要】Based on the theorem about Frattini subgroups of the free products of any set of subgroups with a cyclic a-malgamated subgroup generalized by M. K. Azarian, the corresponding theorems on fn Frattini subgroups and fc Frattini subgroups are proposed and are proved from two different points of view in this paper. Here fn Frattini subgroups and fc Frattini subgroups are defined as the intersection of all maximal normal subgroups and the intersection of all characteristic subgroups respectively and they coincide with the set of fn-nongenerators and the set of fc-nongenerators respectively. This is a further generalization of the results of M. K. Azarian and Q. Guo.%针对Azarian推广的任意多个子群的带循环融合自由积的Frattini子群的定理,提出了相应的关于fnFrattini子群和fcFrattini子群的定理,并且从两个不同角度证明了结果.其中fn Frattini子群和fcFrattini子群分别定义为群的所有具有有限指数的极大正规子群的交和所有具有有限指数的极大特征子群的交,分别等于群的fn-非生成元和fc-非生成元组成的集合.进一步推广了Azarian和郭钦等相关定理.