Noether symmetry approach in matter-dominated cosmology with variable G and Lambda

In the framework of renormalization-group improved cosmologies, we use the Noether symmetry approach to get exact and general integration of the matter-dominated cosmological equations. This is performed by using an expression of Lambda=Lambda(G) determined by the method itself. We also work out a comparison between such a model and the concordance LambdaCDM model as to the magnitude-redshift relationship, hence showing that no appreciable differences occur.