Brown complex

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This article gives a general procedure to construct a complex associated with a group (which may be required to satisfy certain finiteness conditions)Template:Lie analogue

Definition

Given a finite group G, the Brown complex of G is defined as follows. Let p be a prime dividing the order of G and denote by S_p(G) the set of nontrivial p-subgroups of G. The order complex associated with S_p(G) is termed the Brown complex for G.

More explicitly, the Brown complex is a complex where the points are p-subgroups and an r-simplex is a set of p-subgroups of which any two are comparable.

References

  • Euler characteristics of groups by Kenneth S. Brown