Monday, April 5th, 2010
3:00pm - 4:00pm, in Science 2-065

Timothy Kohl

Boston University

Regular Permutation Groups of Order mp

Abstract: For $\Gamma$ a group of order $mp$ for $p > m$ prime, we study the enumeration of the regular permutation subgroups of $Perm(\Gamma)$ normalized by the left regular representation of $\Gamma$. Part of our goal is to determine the number and classes of those regular subgroups, as well as to apply this information to the study of Hopf-Galois structures on separable field extensions $L/K$ with $\Gamma=Gal(L/K)$ since these structures are in one-to-one correspondence with such regular subgroups. This is a generalization of the author's work on the case where $m=4$.