Independence of equational theories and automorphism groups of lattices (Q1071794)

The main result of the paper is the following theorem: Let G be a group, \({\mathfrak M}\) be a nontrivial variety of lattices. Let \(\alpha\) be any cardinal greater than the smallest cardinality of a graph \(\Omega\) for which G is isomorphic to Aut(\(\Omega)\). Then there exists a set \({\mathcal L}\) of \(2^{\alpha}\) pairwise nonisomorphic lattices of cardinality \(\alpha\) such that for every \(L\in {\mathcal L}\), G is isomorphic to Aut(L) and \({\mathfrak M}\) is the variety generated by L.