International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 1, Pages 29-45
doi:10.1155/S0161171280000038
On the Knuth semi-fields
D.R. Hughes
and M.J. Kallaher
Department of Mathematics, Westfield College, University of London, London, United Kingdom
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].