Y. Felix et A. Murillo, A BOUND FOR THE NILPOTENCY OF A GROUP OF SELF HOMOTOPY-EQUIVALENCES, Proceedings of the American Mathematical Society, 126(2), 1998, pp. 625-627
Let E-Omega(X) be the group of homotopy classes of self-homotopy equiv
alences of X such that Omega f similar or equal to 1d(Omega X). We pro
ve that epsilon(Omega)(X) is a nilpotent group and that nil epsilon(Om
ega)(X) less than or equal to cat(X) - 1.