PRIMITIVITY OF FINITE SEMIFIELDS WITH 64 AND 81 ELEMENTS

Abstract

A finite semifield D is a finite nonassociative ring with identity such that the set D * = D \{0} is a loop under the product. Wene conjectured in [1] that any finite semifield is either right or left primitive, i.e. D* is the set of right (or left) principal powers of an element in D. In this paper we study the primitivity of finite semifields with 64 and 81 elements.