Automorphism Groups for Semidirect Products of Cyclic Groups

Abstract

Every semidirect product of groups $K⋊H$ has size $\left|K\right|\cdot \left|H\right|$, yet the size of such a group's automorphism group varies with the chosen action of $H$ on $K$. This paper will explore groups of the form $\text{Aut}(K⋊H)$, considering especially the case where $H$ and $K$ are cyclic. Only finite groups will be considered.

Produced during the 2013 UChicago Mathematics REU