International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 1, Pages 29-45

On the Knuth semi-fields

D. R. Hughes1 and M. J. Kallaher1

1Department of Mathematics, Westfield College, University of London, London, United Kingdom
2Department of Mathematics, Washington State University, Pullman, Washington 99163, USA

Received 28 May 1979; Revised 22 October 1979

Copyright © 1980 D. R. Hughes and M. J. Kallaher. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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].