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.
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)
