Abstract
Let q be an odd prime power, F-q be a finite field of order q and A be a semifield of order q(8) over F-q admitting an elementary group E <= Aut(A) of order 2(3) acting freely on A. In this paper, we investigate these semifields. More precisely, we prove that there is an 8 x 8 matrix (lambda i, j) (i, j. V) of " structure constants" which completely determines A. Many other new results are proved.