2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78336We introduce a pairing structure within the Moore complex NG of a simplicial group G and use it to investigate generators for NG_n\cap D_n where D_n is the subgroup generated by degenerate elements. This is applied to the study of algebraic models for homotopy types.25 pagesAlgebraic TopologyK-Theory and Homology18D35, 18G30 18G50 18G55text