On some flag-transitive non-classical \(c.C_ 2\)-geometries
A \(c.C_ 2\)-geometry is a residually connected geometry which is an extension of a generalized quadrangle by a circle geometry (the intersection property is not assumed). The author constructs five flag- transitive geometries of this type, which appear to be new. These geometries have point sets of sizes 160, 80, 896, 448, 448 (with two pairs of quotients involved). The quadrangle residues of these geometries are isomorphic to the unique quadrangle of order (3,5) or to its dual [cf. \textit{S. E. Payne}, Proc. Boca Raton, 1990, Congr. Numerantium 77, 5- 29 (1990)]. The new geometries are constructed as coset geometries from groups described by generators and relations [cf. the author, Eur. J. Comb. 12, No. 2, 159-181 (1991; Zbl 0735.51011)]. The geometry on 896 points is also constructed from the unitary vector space \(GF(4)^ 8\).
scientific article; zbMATH DE number 167698