The lattices of subgroups and varieties of lattice ordered groups
Mary Elizabeth Huss · Summit (Simon Fraser University) · 1981
ordered group &s a group (G,+) w i t h a l a t t i c e order 5 t h a t ,is dompatible w i t h the group operation.-In Chapter 1 0 t we develop the basic properties of l a t t i c e ordered groups and include a discussion of $-subgroups (sybgrotips which a r e a l s o sublattides) and / -U of ordered permutation-groups.3 * -. d ~ - Th$-second chapter i s devoted t o l a t t i c e s of subgroups of lattice-ohe~& gru-.I n &&&ax weanswer i r queskion-posed -4q-= 2 a = = = -Conrad, showing t h a t the l a t t i c e of 8-subgroups of a l a t t i c e ' ordered g r o ~p , ~ G , ^is d i s t r i b u t i v e i f and only i f G i s isomorphic t o a subgroup of the additive rationals.I I n Chapter 3 we consider several examples of v a r i e t i e s P J of l a t t i c e urdered groups a n d x r e ~ hm-*q-are r e l a t e d i r t h e -l a t t i c e ---3 of v a r i e t i e s of l a t t i c e ordered groups.'W e a l s o d e s c r a e a ' generalization of the wreath prbduct, the twisted wreath product, . .showing t h a t the twisted-wreath product of a l a t t i c e ordered group + by a t o t a l l y .ordered group may he l a t t i c e ordered.W e conclude by..hlooking a t a s p e c i f i c example of a twisted wreath product and see haw I would l i k e to thank D r .N,R, Reilly for h i s encouragement and guidance during the preparation . of t h i s t h e s i s , - I would a l s o like t o thank Mrse, ~ylvia'Holmes for the excellent typing.-. . .