μ-homotopic maps are loop homotopic

Summary In4] we have defined a notion of μ-homotopy in the category of simplicial groups and we have made the conjecture that μ-homotopy is equivalent to loop homotopy. The purpose of this paper is to prove this cojecture. Entrata in Redazione il 25 febbraio 1972. This work was done while the author held a Visiting Professorship at the Istituto Matematico, Università di Perugia, under the auspices of the Italian National Research Council.