Quasinormal subgroups of finite p-groups

Abstract

The distribution of quasinormal subgroups within a group is not particularly well understood. Maximal ones are clearly normal, but little is known about minimal ones or about maximal chains. The study of these subgroups in finite groups quickly reduces to p-groups. Also within an abelian quasinormal subgroup, others (quasinormal in the whole group) abound. But in non-abelian quasinormal subgroups, the existence of others can be dramatically rare.