Counting the generalized twisted fields


In this paper we exploit a theorem of Biliotti, Jha, and Johnson exhibiting a procedure to count the number of non- isotopic generalized twisted fields of orders p<sup>n</sup> where p ≥ 3 which is denoted by g(p<sup>n</sup>).We show that g (p<sup>n</sup>) is a polynomial in p that is sharply bounded below by {n-2 \choose 2}(p-2) and bounded above by a polynomial of degree \lfloor{n \over 2}\rfloor.

DOI Code: 10.1285/i15900932v27n1p53

Keywords: Semifield; Generalized twisted field; Projective plane; Finite geometry

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