Two-generator Frattini subgroups of finitep-groups

This paper deals with nonabelianp-groupsT (p a prime andp>2) which are either metacyclic or Redei. These groups are classified into those which are Frattini subgroups of a finitep-groupG and those which are not. Finally, it is shown that a nonabelian two-generator group of orderp ⁿ (n>4) which is the Frattini subgroup of ap-group must be metacyclic. This work is contained in the author’s dissertation.