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half linearly ordered group; lexicographic product; isomorphic refinements

References:

[1] L. Fuchs: **Partially Ordered Algebraic Systems**. Pergamon Press, Oxford-London-New York-Paris, 1963. MR 0171864 | Zbl 0137.02001

[2] M. Giraudet and F. Lucas: **Groupes à moitié ordonnés**. Fund. Math. 139 (1991), 75–89. MR 1150592

[3] J. Jakubík: **The mixed product decompositions of partially ordered groups**. Czechoslovak Math. J. 20 (1970), 184–206. MR 0258705

[4] J. Jakubík: **On half lattice ordered groups**. Czechoslovak Math. J. 46 (1996), 745–767. MR 1414606

[5] A. I. Maltsev: **On ordered groups**. Izv. Akad. Nauk SSSR, ser. matem., 38 (1951), 473–482. (Russian) MR 0032645