AN EXPONENTIAL BOUND ON THE NUMBER OF NON-ISOTOPIC COMMUTATIVE SEMIFIELDS

被引：4

作者：

Goolog, F. A. R. U. K. ^{[1
]}

Kolsch, L. U. K. A. S. ^{[2
,3
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, PRAGUE, Czech Republic

[2] Univ Rostock, Rostock, Germany

[3] Univ S Florida, Dept Math & Stat, Tampa, FL USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 376卷 / 03期

基金：

美国国家科学基金会;

关键词：

PERFECT; ALGEBRAS; PLANES; FAMILY; POWER;

D O I：

10.1090/tran/8785

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页码：1683 / 1716

页数：34