Automorphisms of Metacyclic p-Groups with Cyclic Maximal Subgroups

Authors

Mark Schulte, St. Olaf CollegeFollow

Abstract

This paper deals with the determination of the automorphism group of the metacyclic p-groups, P(p,m), given by the presentation P(p,m) = where p is an odd prime number. We show that Aut(P) has a unique Sylow p-subgroup, S_p, and that Aut(P) is isomorphic to the the semidirect product of S_p and Z_(p-1).

Author Bio

The research on which this paper is based was completed while I was anundergraduate student at St. Olaf College. I began my project while in anAbstract Algebra II class and completed the remainder of the research as anindependent research project under the direction of Professor Jill Dietz. Igraduated from St. Olaf College in May, 1999 and am currently employed as anactuary. My hobbies include Nordic ski racing, water skiing, andwindsurfing. I plan on returning to graduate school in Fall of 2002 towork towards a Ph.D. in mathematics.

Recommended Citation

Schulte, Mark (2001) "Automorphisms of Metacyclic p-Groups with Cyclic Maximal Subgroups," Rose-Hulman Undergraduate Mathematics Journal: Vol. 2: Iss. 2, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol2/iss2/4