The semilattices of nilextensions of left groups and their varieties (Q1285856)

Several characterizations of the class of semigroups which are semilattices of nilextensions of left groups are given. In particular, this class is defined by the equation \((xy)^\omega(yx)^\omega=(xy)^\omega\). Also, this class as a variety is the semigroup product \(G*R\) of the variety \(G\) of groups and the variety \(R\) of \(\mathcal R\)-trivial semigroups.