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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
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