GROUP-ACTIONS ON FINITE ACYCLIC SIMPLICIAL COMPLEXES

In this paper we develop some homological techniques to obtain fixed p oints for groups acting on finite Z-acyclic complexes. In particular w e show that if a group G acts on a finite 2-dimensional acyclic simpli cial complex D, then the fixed point set of G on D is either empty or acyclic. We supply some machinery for determining which of the two cas es occurs. The Feit-Thompson Odd Order Theorem is used in obtaining th is result.