重庆文理学院学报：自然科学版
重慶文理學院學報：自然科學版
중경문이학원학보：자연과학판
Journal of Chongqing University of Arts and Sciences
2012年
1期
28-30,34
,共4页
psnFrattini子群%pscFrattini子群%psn-非生成元%psc-非生成元%群的融合自由积
psnFrattini子群%pscFrattini子群%psn-非生成元%psc-非生成元%群的融閤自由積
psnFrattini자군%pscFrattini자군%psn-비생성원%psc-비생성원%군적융합자유적
psn Frattini subgroup%psc Frattini subgroup%psn-nongenerators%psc-nongenerators%amalgamated free products of groups
Azarian将Tang得到的关于两个群的带循环融合自由积的Frattini子群的一个定理推广到任意多个子群的带循环融合自由积的情形.文章首先引入任意群G的两种广义Frattini子群,psn Frattini子群和psc Frattini子群,它们分别定义为指数为素数方幂ps的极大正规子群的交和指数为素数方幂ps的极大特征子群的交,其中p为任意素数.然后分别从两个不同角度出发,考虑任意多个子群的带循环融合自由积的psn Frattini子群和psc Frattini子群,得到了类似的结果,从而推广了Azarian和郭钦等人的结果.
Azarian將Tang得到的關于兩箇群的帶循環融閤自由積的Frattini子群的一箇定理推廣到任意多箇子群的帶循環融閤自由積的情形.文章首先引入任意群G的兩種廣義Frattini子群,psn Frattini子群和psc Frattini子群,它們分彆定義為指數為素數方冪ps的極大正規子群的交和指數為素數方冪ps的極大特徵子群的交,其中p為任意素數.然後分彆從兩箇不同角度齣髮,攷慮任意多箇子群的帶循環融閤自由積的psn Frattini子群和psc Frattini子群,得到瞭類似的結果,從而推廣瞭Azarian和郭欽等人的結果.
Azarian장Tang득도적관우량개군적대순배융합자유적적Frattini자군적일개정리추엄도임의다개자군적대순배융합자유적적정형.문장수선인입임의군G적량충엄의Frattini자군,psn Frattini자군화psc Frattini자군,타문분별정의위지수위소수방멱ps적겁대정규자군적교화지수위소수방멱ps적겁대특정자군적교,기중p위임의소수.연후분별종량개불동각도출발,고필임의다개자군적대순배융합자유적적psn Frattini자군화psc Frattini자군,득도료유사적결과,종이추엄료Azarian화곽흠등인적결과.
M.K.Azarian generalized a theorem on Frattini subgroups of amalgamated free products of two subgroups proposed by C.Y.Tang to the case of the free product of any set of subgroups with amalgamated subgroup.Now as a first step two types of generalized Frattini subgroups,psn Frattini subgroups and psc Frattini subgroups are introduced.They are defined as the intersection of all maximal normal subgroups and the intersection of all maximal characteristic subgroups respectively.Then psn Frattini subgroups and psc Frattini subgroups of the free product of any set of subgroups with amalgamated subgroup being cyclic are considered from two different points of view and similar results are obtained,which are a generalization of the results of M.K.Azarian and Q.Guo.
