This project is concerned with finite geometries and groups. There are four areas which will be considered. The principal investigator will extend previous work on embeddings and hyperplanes of point-line geometries; work on characterizing parapolar spaces; study new cases of the connections between m-spreads and constructions of generalized quadrangles; and see if frames can be used to generate the full Lie incidence geometry. The principal investigator will attempt in all the above work to understand groups by how they act on geometries. The research in this project involves the interplay between finite dimensional geometry and the actions of groups of transformations on these geometries. This work has implications for the structure of finite groups, for algebraic coding theory, and for finite geometry. ***
