On the Knuth semi-fields

Abstract

We consider three of Knuth's four classes of semi-fields—Knuth [11]—namely, those having dimension 2 over a nucleus and show that the autotopism group is solvable (Corollary 4.12). This generalizes a result of Hughes [5]. We also show that for semi-fields of dimension 2 over a nucleus, the number of pairwise non-isomorphic isotopic images is at least 5 (Corollary 5.1.1). This generalizes a result in [10].