The structure of lattices of nilsemigroup varieties (Q2755750)

The authors prove that for every variety \(\mathcal V\) of nilsemigroups, the subvariety lattice of \(\mathcal V\) is antiisomorphic to a sublattice of the direct product of congruence lattices of certain \(G\)-sets (i.e., sets in which an action of the group \(G\) is defined). Given \(\mathcal V\), the \(G\)-sets in question can be explicitly calculated. As an example, this result is used in order to analyze identities in the subvariety lattice of the variety \(\mathcal N\) defined by the identities \(xyzt=tzyx\), \(x^2y=(xy)^2\), \(xy^2=yx^2\), \(xyzx=yxzx\), \(x^4=0\).