Abstract
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 is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ja. Berkovic,A generalization of the theorems of Hall and Blackburn and their applications to nonregular p-groups. Math USSR-Izv.5(1971), 829–832.
C. Hobby,The Frattini subgroup of a p-group, Pacific J. Math.10 (1960), 209–212.
C. Hobby,Generalizations of a theorem of N. Blackburn on p-groups, Illinois J. Math.5 (1961).
B. Huppert,Endliche Gruppen I, Springer-Verlag, Berlin, 1967.
G. Lange, Doctoral dissertation, University of New Hampshire, 1975.
Author information
Authors and Affiliations
Additional information
This work is contained in the author’s dissertation.
Rights and permissions
About this article
Cite this article
Lange, G.L. Two-generator Frattini subgroups of finitep-groups. Israel J. Math. 29, 357–360 (1978). https://doi.org/10.1007/BF02761173
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02761173