Geodesic
Soluble Groups and Varieties of $l$-Groups
Algebra i logika, Tome 44 (2005) no. 3, pp. 355-367.

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A sufficient condition is given under which factors of a system of normal convex subgroups of a linearly ordered (l. o. ) group are Abelian. Also, a sufficient condition is specified subject to which factors of a system of normal convex subgroups of an l. o. group are contained in a group variety $\mathcal V$. In particular, for every soluble l. o. group $G$ of solubility index $n$, $n\geqslant2$, factors of a system of normal convex subgroups are soluble l. o. groups of solubility index at most $n-1$. It is proved that the variety $\mathcal R$ of all lattice-ordered groups, approximable by linearly ordered groups, does not coincide with a variety generated by all soluble l. o. groups. It is shown that if $\mathcal V$ is any $o$-approximable variety of $l$-groups, and if every identity in the group signature is not identically true in $\mathcal V$, then $\mathcal V$ contains free l. o. groups.
Keywords: variety of $l$-groups
Mots-clés : soluble group. 
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     title = {Soluble {Groups} and {Varieties} of $l${-Groups}},
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N. Ya. Medvedev. Soluble Groups and Varieties of $l$-Groups. Algebra i logika, Tome 44 (2005) no. 3, pp. 355-367. http://geodesic.mathdoc.fr/item/AL_2005_44_3_a4/

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