Given a finite group , the Brown complex of is defined as follows. Let be a prime dividing the order of and denote by the set of nontrivial -subgroups of . The order complex associated with is termed the Brown complex for .
More explicitly, the Brown complex is a complex where the points are -subgroups and an -simplex is a set of -subgroups of which any two are comparable.
- Euler characteristics of groups by Kenneth S. Brown