Geodesic
Lexicographic extensions and $pl$-groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1133-1138 
E. E. Shirshova. Lexicographic extensions and $pl$-groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1133-1138. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a26/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is known that a lexicographic extension of an $l$-group by an $l$-group needs not to be an $l$-group. It has been proved in [7] that such extension is a $pl$-group (introduced in [2] and [4]). The purpose of this paper is to show that the class of $pl$-groups is closed with respect to lexicographic extensions.

[1] Kopytov V. M., Reshetochno uporyadochennye gruppy., Nauka, M., 1984 | MR | Zbl

[2] Conrad P., “Representation of partially ordered abelian groups as groups of real valued functions”, Acta Math., 116 (1966), 199–221 | MR | Zbl

[3] Conrad P., Teller J. R., “Abelian pseudo lattice ordered groups”, Publ. Math. Debrecen., 17 (1970), 223–241 | MR

[4] Shirshova E. E., “O psevdo strukturno uporyadochennykh gruppakh”, Gruppy i moduli. Teoriya igr, Sb. tr., M., 1973, 10–18 | MR

[5] Fuks L., Chastichno uporyadochennye algebraicheskie sistemy, Mir, M., 1965 | MR

[6] Teller J. R., “On extensions of lattice-ordered groups”, Pacif. J. Math., 14 (1964), 709–718 | MR | Zbl

[7] Shirshova E. E., “On extensions of $po$-groups. Part 1”, Contemporary Mathematics, 131 (1992), 345–353 | MR | Zbl