In this article, we present general properties of fixed-point groups of the automorphisms of finite groups. Specifically, we determine the form of fixed-point groups and partition $\aut(G)$ according to the number of fixed points possessed by each automorphism. A function $\theta$ records the size of each partitioning set; we find properties for $\theta$ in general and develop formulae for $\theta$ with respect to certain classes of finite abelian groups.
Jill Dietz, Department of Mathematics, St. Olaf College email@example.com
Checco, James; Darling, Rachel; Longfield, Stephen; and Wisdom, Katherine
"On the Fixed Points of Abelian Group Automorphisms,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 11
, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol11/iss2/3