An exponential bound on the number of non-isotopic commutative semifields

We show that the number of non-isotopic commutative semifields odd order p n p^{n} is exponential in alttext="n"> encoding="application/x-tex">n when alttext="n equals 4 t"> = 4 t encoding="application/x-tex">n = 4t and alttext="t"> encoding="application/x-tex">t not a power alttext="2"> 2 encoding="application/x-tex">2 . introduce new family method for proving isotopy results on we use to deduce aforementioned bound. The previous best bound was quadratic given by Zhou Pott [Adv. Math. 234 (2013), pp. 43–60]. Similar bounds case even were Kantor [J. Algebra 270 (2003), 96–114] Williams [Trans. Amer. Soc. 356 (2004), 895–938].