Automorphism Groups of some Finite Semifields

We determine the automorphism group for some well known constructions of finite semifields. In particular, we compute the automorphism group of Sandler's semifields and in certain cases the automorphism groups of the Hughes-Kleinfeld and Knuth semifields. We also determine how many nonisomorphic Sandler semifields can be constructed given a finite field F and a finite extension L/F.