# zbMATH — the first resource for mathematics

On three questions in the theory of l-varieties. (Russian) Zbl 0755.06010
A variety of lattice-ordered groups $$\mathcal V$$ is called divisible if every $$\ell$$-group $$G$$ in $$\mathcal V$$ can be embedded as an $$\ell$$-subgroup in a divisible $$\ell$$-group $$G^*$$ in $$\mathcal V$$. The main results of the paper are: There is a continuum of non-divisible varieties of nilpotent $$\ell$$- groups. There is a continuum of divisible varieties of nilpotent $$\ell$$- groups. The variety of rigid $$\ell$$-groups has basis rank 2.
##### MSC:
 06F15 Ordered groups
Full Text: