fnFrattini Subgroups and fcFrattini Subgroups of Amalgamated Free Products of Groups
Zhirang Zhang · Journal of Chengdu University of Information Technology · 2011
Based on the theorem about Frattini subgroups of the free products of any set of subgroups with a cyclic amalgamated subgroup generalized by M.K.Azarian,the corresponding theorems on fnFrattini subgroups and fcFrattini subgroups are proposed and are proved from two different points of view in this paper.Here fnFrattini subgroups and fcFrattini 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.