  A p-local finite group is an algebraic structure with a classifying space
which has many of the properties of p-completed classifying spaces of finite
groups. In this paper, we construct a family of 2-local finite groups, which
are exotic in the following sense: they are based on certain fusion systems
over the Sylow 2-subgroup of Spin_7(q) (q an odd prime power) shown by Solomon
not to occur as the 2-fusion in any actual finite group. Thus, the resulting
classifying spaces are not homotopy equivalent to the 2-completed classifying
space of any finite group. As predicted by Benson, these classifying spaces are
also very closely related to the Dwyer-Wilkerson space BDI(4).
  Erratum (11 Feb 2005). An error in the paper was pointed out to the authors
by Andy Chernak. The error is corrected in the erratum at the end of version 2,
which should be read alongside the paper.
