Every finite group is the group of self-homotopy equivalences of an elliptic space
Every finite group is the group of self-homotopy equivalences of an elliptic space
We prove that every finite group G can be realized as the group of self-homotopy equivalences of infinitely many elliptic spaces X. To construct those spaces we introduce a new technique which leads, for example, to the existence of infinitely many inflexible manifolds. Further applications to representation theory will appear …