Finite flag-transitive projective planes: A survey and some remarks
The main problem which is discussed in this paper is the characterization of finite Desarguesian planes by certain transitivity properties. Most of the paper provides a detailed outline on the subject of flag-transitive projective planes. In particular considerable results obtained on this topic by Ostrom, Wagner, Ott, McLaughlim, Higman, Roth, Feit, Fink and others are reported. These results are split up in two categories: those established before \(1980\) (obtained essentially by geometrical methods) and those established after \(1980\) (obtained by using group theory and pure algebra). In the last part of the paper, the author considers polarities of projective planes admitting an abelian Singer group. Some new results in case the full automorphism group of the plane acts semiregularly on the flags are obtained.
characterization of finite Desarguesian planes
scientific article; zbMATH DE number 1924781