On the Fixed Points of Abelian Group Automorphisms
نویسندگان
چکیده
In this article, we present general properties of xed-point groups of the automorphisms of nite groups. Speci cally, we determine the form of xed-point groups and partition Aut(G) according to the number of xed points possessed by each automorphism. A function θ records the size of each partitioning set; we nd properties for θ in general and develop formulae for θ with respect to certain classes of nite abelian groups. Acknowledgements: The authors did this work under Professor Jill Dietz in the Directed Undergraduate Research course in the fall of 2009, and would like to thank St. Olaf College for supporting this research. Page 50 RHIT Undergrad. Math. J., Vol. 11, No. 2
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