On Dowling geometries of infinite groups

On Dowling geometries of infinite groups

A finite subgeometry of a Dowling geometry for an infinite group is exhibited, which cannot be embedded in a Dowling geometry for any finite group; this provides a negative answer to a question of Bonin. The question addressed herein is motivated by the following fundamental result of Rado, concerning the embeddability of finite geometries in projective geometries [Ra, Theorem 4]: Theorem. Ever...

Dowling group geometries and the critical problem

This paper relates the critical problem of Crapo and Rota [ " On the Foundations of Combinatorial Theory: Combinatorial Geometries, " M.I.T. Press, Cambridge, MA, 19703 to Dowling group geometries. If A is a finite group, Q,(A) is the rank-r Dowling group geometry over A, and M is a rank-r matroid embeddable as a minor of Q,(A), then it is shown that the critical exponent of M over A is well de...

On Infinite Groups

On Automorphism Groups of Parabolic Geometries

On geometries of the Fischer groups

The Fischer groups Fi22, Fi23 and Fi24 are associated with a number of diagram geometries, some of which have been characterized recently. Exploiting a relationship between these geometries we obtain some further characterizations.