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.

Author Bio

James Checco is a senior mathematics and chemistry major. James will be attending the University of Wisconsin - Madison to study chemistry.

Rachel Darling is a junior mathematics major who hopes to go to graduate school after next year. This was her first experience with undergraduate research. Rachel also runs track and cross country and enjoys just being outdoors.

Stephen Longfield is a senior mathematics major and statistics concentrator who will be attending University of Illinois-Urbana next fall to pursue a doctorate in mathematics.

Katherine Wisdom will be graduating in 2010 with degrees in Math Education and Music. She plans on pursuing further education in Civil Engineering and enjoys playing the flute.