Geodesic
The structure of lattice-ordered commutative topological groups of compact origin
Matematičeskie zametki, Tome 21 (1977) no. 6, pp. 855-860.

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It is shown that every lattice-ordered commutative separable topological group of compact origin can be obtained from a finite number of its linearly ordered subgroups, each of which is isomorphic either to the additive group of real numbers with the natural topology and the usual order or to a subgroup of the additive group of real numbers with the discrete topology and the usual order, admitting a finite system of linearly independent generators, by forming in turn the direct and the lexicographic products. 
@article{MZM_1977_21_6_a12,
     author = {A. N. Islamov},
     title = {The structure of lattice-ordered commutative topological groups of compact origin},
     journal = {Matemati\v{c}eskie zametki},
     pages = {855--860},
     publisher = {mathdoc},
     volume = {21},
     number = {6},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a12/}
}
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A. N. Islamov. The structure of lattice-ordered commutative topological groups of compact origin. Matematičeskie zametki, Tome 21 (1977) no. 6, pp. 855-860. http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a12/