Perhaps the most important difference between the old and the new geometry lies in the extended use made during the present century of geometric transformations, f The change which has come about in this direction is due in part to the influence of certain branches of applied mathematics in which one has to deal not merely with geometric configurations but also with certain changes which these ...

Let ~ be a (possibly infinite) projective plane, and G a collineation group of ~ . Suppose temporarily that ~ is a translation plane with respect to L, and G is the group of collineations fixing L. Then G=TGx, where T is the translation group with respect to L, and x is an affine point. If, moreover, the characteristic of ~ is not 2, then Gx= CG(t) and G= TCa(t), where t is an involutory homolo...

This paper is devoted to study the symmetries of the energymomentum tensor for the static spacetimes with maximal symmetric transverse spaces. We solve matter collineation equations for the four main cases by taking one, two, three and four non-zero components of the vector ξ. For one component non-zero, we obtain only one matter collineation for the non-degenerate case and for two components n...

Finite translation planes having a collineation group isomorphic to SL(2, 5)occur in many investigations on minimal normal non-solvable subgroups of linear translation complements. In this paper, we are looking for multiply derived translation planes of the desarguesian plane which have an inherited linear collineation group isomorphic to SL(2, 5). The Hall plane and some of the planes discover...

Let G be a collineation group of a thick finite generalised hexagon or generalised octagon Γ. If G acts primitively on the points of Γ, then a recent result of Bamberg et al. shows that G must be an almost simple group of Lie type. We show that, furthermore, the minimal normal subgroup S of G cannot be a Suzuki group or a Ree group of type G2, and that if S is a Ree group of type F4, then Γ is ...