Wednesdays, February 1 & 8
Milner 317, 12:30 PM
Title: Orbits of normal basis generators I & II
Abstract: These talks will be based on my paper by the same title [Q. J. Math. 55 (2004), no. 2, 203--206]. Let L/K be a finite-dimensional Galois field extension with Galois group G, B the set of normal basis generators for this extension, and C = {gamma in L | gamma.B=B}. Then C is a group under multiplication. This group was introduced and characterized in Theorem 1.15 of a well-known paper by H. W. Lenstra, Jr. and R. Schoof "Primitive normal bases for finite fields" [Math. Comp. 48 (1987), no. 177, 217--231]. The result was stated in that paper without proof. The purpose of my talk is to give a proof of the theorem.