论文标题
计算非异位Taniguchi半场的数量
Counting the number of non-isotopic Taniguchi semifields
论文作者
论文摘要
我们研究了Taniguchi半场的同位素问题。当两个Taniguchi半场是同位素时，我们给出一个完整的表征。我们进一步提供了非异位Taniguchi semifields总数的精确上限和下限，证明大约有$ p^{m+s} $非异位Taniguchi taniguchi semifields smize $ p^{2M} $，$ s $是$ s $的最大划分，是$ m $ $ m $ a $ a $ 2s $ 2s \ neq m $。该结果证明，塔尼古奇半场（Taniguchi Semivields）家族（渐近地）是已知的奇数最大家族。证明的关键要素是确定使用组理论来利用半场自动化组的某些大亚组的存在的技术。
We investigate the isotopy question for Taniguchi semifields. We give a complete characterization when two Taniguchi semifields are isotopic. We further give precise upper and lower bounds for the total number of non-isotopic Taniguchi semifields, proving that there are around $p^{m+s}$ non-isotopic Taniguchi semifields of size $p^{2m}$ where $s$ is the largest divisor of $m$ with $2s\neq m$. This result proves that the family of Taniguchi semifields is (asymptotically) the biggest known family of semifields of odd order. The key ingredient of the proofs is a technique to determine isotopy that uses group theory to exploit the existence of certain large subgroups of the autotopism group of a semifield.
