This award will support collaborative research in mathematics between Dr. Andrew Glass, Bowling Green State University and Dr. J.S. Wilson, University of Cambridge, England. Linearly ordered groups are the building blocks for partially ordered groups, yet very few examples or constructions are known. Recently, Dr. Glass and Dr. Wilson have shown that linearly ordered groups arise naturally in the investigation of certain doubly homogeneous groups of automorphisms of linearly ordered sets. This already answers several questions concerning lattice-ordered groups and provides a link between Hahn's Theorem for Abelian linearly ordered groups and permutation groups. Glass and Wilson plan to use this connection as well as some recent constructions of infinite groups in the study of automorphism groups. Wilson's research has been almost exclusively in constructions of infinite soluble groups, whereas Glass's has been primarily in automorphism groups of linearly ordered sets and their applications. Their areas of expertise are complementary and their joint work could lead to considerable advances in this subject.
