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Abstract
The aim of this article is to investigate the nuclei of a semifield A of order q 4, q is a power of 2, admitting a four-group E of automorphisms isomorphic to Z 2 × Z 2 acting freely on A and having GF(q 2) in its left nucleus. We also study the dual semifield A* of A and show that A and A* are isomorphic.
ACKNOWLEDGMENT
The authors wish to thank Schaeffer for his helpful discussion, and to the referee for his suggestions to modify the proof of Theorem 3.3.
Notes
Communicated by I. P. Shestakov.