  We formulate a "correct" version of the Quillen conjecture on linear group
homology for certain arithmetic rings and provide evidence for the new
conjecture. In this way we predict that the linear group homology has a direct
summand looking like an unstable form of Milnor K-theory and we call this new
theory "homological symbols algebra". As a byproduct we prove the Quillen
conjecture in homological degree two for the rank two and the prime 5.
