Explorations in Automorphism Groups

Date of Graduation

Summer 2004

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Abstract

This body of work sets out to explore various properties of automorphism groups. We show explicit calculations of the automorphism groups of cyclic groups, permutation groups, dihedral groups, and generalized quaternion groups. We also calculate the order of the automorphism groups of non-cyclic abelian groups. We thn show the explicit calculation of all automorphism groups of order less than sixteen. After all this calculation, we switch to the "inverse problem." Namely, we find groups which have a particular automorphism group in common. We show a complete method for how to find groups which share a cyclic automorphism group. We then exhibit which groups share S₃ as an automorphism group and which groups share S₄ as an automorphism group. We close by specifying areas of research on this topic which have not been covered in this thesis.

Keywords

abelian, algebra, automorphism, cyclic, dihedral, group, inverse problem, permutation, quaternion, symmetric

Subject Categories

Mathematics

Copyright

© Jeremy A. Osborne

Citation-only

Dissertation/Thesis

Share

COinS