<i>p</i>-Groups with an Abelian Maximal Subgroup and Cyclic Center

Abstract

Abstract All such nonabelian finite p -groups are classified. They coincide with the class of nonabelian finite p -subgroups of GL(p, F) , where F is a field, not of characteristic p , which contains all p power roots of 1, or agian with the class of all nonabelian finite subgroups of Z p = wr Z p . Various automorphism groups associated to them and their representations are calculated. Two such subgroups of GL(p, F) are conjugate as subgroups of GL(p, F) iff they are isomorphic.