Geodesic
On convex directed subgroups of pseudo lattice-ordered groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 239-252

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We show that all convex directed subgroups of a $pl$-group form a distributive lattice under inclusions that is a Brouwer lattice. We succeeded in extending some $l$-group results concerning rectifying and regular subgroups to the class of $\mathcal{AO}$-groups. Necessary and sufficient conditions are given for an element of a $pl$-group to be an element with a unique value. In order to prove this, some properties of lexicographic extensions of $\mathcal{AO}$-groups and $pl$-groups are investigated. 
@article{FPM_2019_22_4_a15,
     author = {E. E. Shirshova},
     title = {On convex directed subgroups of pseudo lattice-ordered groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {239--252},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a15/}
}
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E. E. Shirshova. On convex directed subgroups of pseudo lattice-ordered groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 239-252. http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a15/