Varieties generated by simple \(l\)-groups (Q1174015)

A lattice-ordered group without nontrivial invariant convex \(\ell\)- subgroups is simple. In this paper the following main results are obtained: Theorem 1. Let \(G\) be a simple non-representable \(\ell\)-group and \(\hbox{var}_ \ell G\) be the \(\ell\)-variety generated by \(G\). Then \(\hbox{var}_ \ell G\) is equal to the \(\ell\)-variety of normal-valued \(\ell\)-groups \(\mathfrak N_ \ell\) or to the \(\ell\)-variety of all \(\ell\)- groups \(\mathcal L\). Some examples of normal-valued simple \(\ell\)-groups are given.