Sylow-like theorems in geometry and algebra

Abstract

The notion of congruence provides a means to extend the Sylow theorems from group theory to a class of geometric structures called congruence spaces and to their corresponding loops. The extension of these results depends on the existence of a group acting transitively on the congruence space and preserving congruence. A partial ordering on the congruence spaces suggests a means to form all of these spaces from groups.