\indent one-parameter convolution semigroups of probability measures on euclidean space are related to limits of partial products of infinitesimal triangular systems of measures, in the sense that such limits are embeddable into one-parameter convolution semigroups. it is a long-standing problem related to the central limit theorem that on an arbitrary locally compact group such a result cannot be tackled unless the infinitesimal system is commutative and additional conditions on the underlying group and/or the limiting measure are satisfied. we shall develop the main steps towards the solution of the problem of embeddable limits and connect the problem with the embedding of infinitely divisible probability measures on the group. the problem, in full generality, is still open.