Basic and degenerate pregeometries (Q427805)

The authors study pairs \((\Gamma,G)\), where \(\Gamma\) is a Buekenhout-Tits pregeometry with connected rank 2 truncation, and \(G\leq\Aut\Gamma\) is transitive on the set of elements of each type. The family of such pairs is closed under forming quotients with respect to \(G\)-invariant type-refining partitions of the element set of \(\Gamma\). The authors indentify the basic pairs (those that admit no nondegenerate quotients), and show, by studying quotients and direct decompositions, that the study of basic pregeometries reduces to examining those where the group \(G\) is faithful and primitive on the set of elements of each type. The authors also study a special case of normal quotients.