Nilpotency and localization of groups of fibre homotopy equivalences (Q2734862)

For a fibration in which certain finiteness conditions hold, it is shown that the group of fibre homotopy equivalences which induce the identity on the homotopy groups of the fibre is solvable. Further, if it is nilpotent, then for any set of primes, the localization of the groups gives the group of the localizations of the spaces. Some applications to the self equivalences of diagrams are obtained.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00050].