New examples of wild nearfields via regular matrix groups over skew polynomial rings

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• 作者：Matthias Grüninger
• 关键词：Nearfields ; Skew fields ; Skew polynomials ; Nagao’s theorem
• 刊名：Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：57
• 期：4
• 页码：789-808
• 全文大小：519 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra
  Convex and Discrete Geometry
  Geometry
  Algebraic Geometry
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2191-0383
• 卷排序：57

文摘

We use Nagao’s Theorem to construct matrix subgroups of dimension 2 over skew polynomial rings acting sharply transitively on the projective line of the quotient skew field. This way we get new examples of nearfields. Under additional conditions we prove that these nearfields are wild nearfields, by which we mean that they are not Dickson nearfields. To our knowledge these are the first known examples of nearfields of dimension greater than 2 over their kernel for which it could be certainly proven that they are wild.