2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159065The homology of GL_n(F) and SL_n(F) is studied, where F is an infinite field. Our main theorem states that the natural map H_4(GL_3(F), k) --> H_4(GL_4(F), k) is injective where k is a field with char(k) \neq 2, 3. For algebraically closed field F, we prove a better result, namely, H_4(GL_3(F), Z) --> H_4(GL_4(F), Z) is injective. We will prove a similar result replacing GL by SL. This is used to investigate the indecomposable part of the K-group K_4(F).26 pages, LatexK-Theory and Homology19D55;19D45text