  The 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).
