Here we solve a number of major open problems concerning computational properties of products and commutators of two ‘transitive’ (but not ‘symmetric’) standard modal logics (such as, e.g., K4, S4, S4.1, Grz, or GL) by showing that all of them are undecidable and lack the (abstract) finite model property. Some of these products turn out to be even not recursively enumerable and some commutators...
