AN ACTION OF A FINITE GROUP ON AN w-CELL WITHOUT STATIONARY POINTS

If G is a transformation group on a space X, then x(~X is a stationary point if gx = x for every g £ G . It has been an open problem, proposed by Smith [5] and by Montgomery [l, Problem 39], to determine whether every compact Lie group acting on a cell or on Euclidean space has a stationary point. Smith [4; 5] has shown the answer to be in the affirmative in case G is a toral group or a finite group of prime power order. In this note we give a simplicial action of A^ the group of even permutations on five letters, on an n-cell without stationary points. Greever [3] has recently shown that the only finite groups of order less than 60 which could possibly act simplicially on a cell without stationary points are a certain class of groups of order 36. We wish to thank P. E. Conner for his help and encouragement.