On Cover-Avoiding Subgroups of Sylow Subgroups of Finite Groups

Abstract

A subgroup H of a finite group G is called to have the cover-avoidance property in G, H is a CAP subgroup of G in short, if H either covers or avoids every chief factor of G. In the present work, we fix a subgroup D in every Sylow subgroup P of F* (G) satisfying 1 <|D| < |P | and study the structure of G under the assumption that every subgroup H with |H | = |D| has the cover-avoidance property in G. We state our results in the broader context of formation theory.