A question on partial CAP-subgroups of finite groups

Autores UPV
Revista Science China Mathematics


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.