Given a finite generalized quadrangle Q, an extended generalized quadrangle is called an extension of Q if each point-residue is isomorphic to Q. There are several known examples of extended generalized quadrangles [4, §1.1], among which those admitting flag-transitive automorphism groups have been extensively studied in their close relations with group theory. Those flag-transitive geometries ...

This paper is a continuation of Kantor (4, 6] and Ronan [10]. We will construct finite and infinite 'geometries' admitting flag-transitive groups and having buildings as universal covers. The first building is that of {1+ (6, (Ji2); the remaining ones are new and strange. As in the aforementioned papers, our motivation is the search for finite geometries that strongly resemble buildings, and fo...

In this paper, a characterisation is given of finite s-arc transitive Cayley graphs with s ≥ 2. In particular, it is shown that, for any given integer k with k ≥ 3 and k 6= 7, there exists a finite set (maybe empty) of s-transitive Cayley graphs with s ∈ {3, 4, 5, 7} such that all s-transitive Cayley graphs of valency k are their normal covers. This indicates that s-arc transitive Cayley graphs...