$$\lambda $$-fold near-factorizations of groups

We initiate the study of $$\lambda $$ λ -fold near-factorizations of groups with $$\lambda > 1$$ λ > 1 . While $$\lambda $$ λ -fold near-factorizations of groups with $$\lambda = 1$$ λ = 1 have been studied in numerous papers, this is the first detailed treatment for $$\lambda > 1$$ λ > 1 . We establish fundamental properties of $$\lambda $$ λ -fold near-factorizations and introduce the notion of equivalence. We prove various necessary conditions of $$\lambda $$ λ -fold near-factorizations, including upper bounds on $$\lambda $$ λ . We present three constructions of infinite families of $$\lambda $$ λ -fold near-factorizations, highlighting the characterization of two subfamilies of $$\lambda $$ λ -fold near-factorizations. We discuss a computational approach to $$\lambda $$ λ -fold near-factorizations and tabulate computational results for abelian groups of small order.