| For any type of abstract algebra, a variety is an equationally defined class of such algebras. Recently varieties of lattice ordered groups (L-groups) have been found to be of interest and this thesis continues their study.; For any L-group G, G x Z denotes the product of G with the integers Z, ordered lexicographically from the right. For a variety V of L-groups let V('L) = Var(G x Z (VBAR) G (epsilon) G). It has been an open question as to whether or not V('L) = V, for every variety V of L-groups. Examples are given to answer this question negatively, and properties of the varieties V('L) are developed.; For a variety V, another closely associated variety is the variety V('R), obtained by reversing the order of the L-groups in V. It is shown that there are varieties for which V('R) (NOT=) V and that the mapping (theta): V (TURNST) V('R) is both a lattice and semigroup automorphism of the set of varieties of L-groups.; Kopytov and Medvedev, and independently Reilly and Feil, have shown that there are uncountably many L-group varieties. By considering further uncountable collections of varieties of L-groups; it is shown that the breadth of the lattice of representable L-groups has cardinality of the continuum. |
