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. 
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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/

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