Quasi-equational bases for graphs of semigroups, monoids and groups

The graph of an algebra A is the relational structure G(A) in which the relations are the graphs of the basic operations of A. Let denote by [inline-graphic not available: see fulltext] the class of all graphs of algebras from a class [inline-graphic not available: see fulltext]. We prove that if [inline-graphic not available: see fulltext] is a class of semigroups possessing a nontrivial member with a neutral element, then [inline-graphic not available: see fulltext] does not have finite quasi-equational basis. We deduce that, for a class [inline-graphic not available: see fulltext] of monoids or groups with a nontrivial member, [inline-graphic not available: see fulltext] also does not have finite quasi-equational basis.