Construction of two-dimensional flag-transitive planes

✍ Scribed by R. D. Baker; G. L. Ebert

• Publisher: Springer
• Year: 1988
• Tongue: English
• Weight: 291 KB
• Volume: 27
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00181610

✦ Synopsis

An affine plane is called flag-transitive if it admits a collineation group which acts transitively on the incident point-line pairs. It has been shown that finite flag-transitive planes are necessarily translation planes, and much work has been devoted to this class of translation planes in recent years. All flag-transitive groups of finite affine planes have been determined, and an infinite family of non-Desarguesian flag-transitive planes has been found, In this paper a method is given for constructing all two-dimensional flag-transitive planes of odd order, subsuming the infinite family mentioned above.