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.
Cite this article
Yangming Li, On Cover-Avoiding Subgroups of Sylow Subgroups of Finite Groups. Rend. Sem. Mat. Univ. Padova 123 (2010), pp. 249–258DOI 10.4171/RSMUP/123-13