MINIMAL NONABELIAN AND MAXIMAL SUBGROUPS OF A FINITE p-GROUP

The p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal class, are classified (Theorem 2.1). For the main result of [CP] and [ZAX] classifying the p-groups all of whose proper nonabelian subgroups are metacyclic, we offer a proof which is shorter and not so involved. In conclusion we study, in some detail, the p-groups containing an abelian maximal subgroup.