The non-existence of sharply 2-transitive sets of permutations in 1"> \(\mathrm {Sp}(2d,2)\) of degree 详细信息    查看全文

• 作者：Dominik Barth
• 关键词：Sharply transitive set ; Symplectic and Orthogonal Groups
• 刊名：Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：58
• 期：1
• 页码：201-209
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra; Geometry; Algebraic Geometry; Convex and Discrete Geometry;
• 出版者：Springer Berlin Heidelberg
• ISSN：2191-0383
• 卷排序：58

文摘

We use Müller and Nagy’s method of contradicting subsets to give a new proof for the non-existence of sharply 2-transitive subsets of the symplectic groups \(\mathrm {Sp}(2d,2)\) in their doubly-transitive actions of degrees \(2^{2d-1}\pm 2^{d-1}\). The original proof by Grundhöfer and Müller was rather complicated and used some results from modular representation theory, whereas our new proof requires only simple counting arguments.