Counting the generalized twisted fields

Abstract

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 $pⁿ$ where $p ≥ 3$ which is denoted by $g(pⁿ)$.We show that $g (pⁿ)$ 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 $\lfloor{n \over 2}\rfloor$.