A question on partial CAP-subgroups of finite groups  

作　　者：BALLESTER-BOLINCHES Adolfo ESTEBAN-ROMERO Ramón LI YangMing 

机构地区：[1]Departament d'Àlgebra,Universitat de València,Burjassot 46100,València,Spain [2]Institut Universitari de Matemàtica Pura i Aplicada,Universitat Politècnica de València,València 46022,Spain [3]Department of Mathematics,Guangdong University of Education,Guangzhou 510310,China

出　　处：《Science China Mathematics》2012年第5期961-966,共6页中国科学：数学（英文版）

基　　金：supported by MEC of Spain,FEDER of European Union (Grant No.MTM-2007-68010-C03-02);MICINN of Spain (Grant No. MTM-2010-19938-C03-01);National Natural Science Foundation of China (Grant No. 11171353/A010201);Natural Science Fund of Guangdong (Grant No.S2011010004447)

摘　　要：A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series.The structural impact of the partial cover and avoidance property of some distinguished subgroups of a group has been studied by many authors.However,there are still some open questions which deserve an answer.The purpose of the present paper is to give a complete answer to one of these questions.A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series.The structural impact of the partial cover and avoidance property of some distinguished subgroups of a group has been studied by many authors.However,there are still some open questions which deserve an answer.The purpose of the present paper is to give a complete answer to one of these questions.

关 键 词：finite groups minimal subgroups partial cover and avoidance property saturated formations 

分 类 号：O152.1[理学—数学] TP393.08[理学—基础数学]