Geodesic
A Subsemilattice of the Lattice of Varieties of Lattice Ordered Groups
Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1309-1318

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Each variety of lattice ordered groups determines a variety of groups, namely the variety of groups generated by the groups i n . In this paper a completely new and different correspondence between varieties of groups and varieties of lattice ordered groups is developed. It is known that the variety of representable lattice ordered groups is defined by the law z + Λ u -1 z - u = 1. Here we consider the varieties defined by laws of this form where u is restricted to lie in some fully invariant subgroup of the free group Fx on a countable set X. All the varieties considered contain the variety of representable l-groups and therefore the free group with appropriate ordering. 
Reilly, Norman R. A Subsemilattice of the Lattice of Varieties of Lattice Ordered Groups. Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1309-1318. doi: 10.4153/CJM-1981-099-2
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