Correction to: Construction of 2–local finite groups of a type studied by Solomon and Benson

Abstract

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 our earlier paper, we constructed 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 ${Spin}_7\left(q\right)$ ($q$ an odd prime power) shown by Solomon not to occur as the 2–fusion in any actual finite group. As predicted by Benson, the classifying spaces of these 2–local finite groups are very closely related to the Dwyer–Wilkerson space $BDI\left(4\right)$. An error in our paper was pointed out to us by Andy Chermak, and we correct that error here.