The mod- p lower central series and the Adams spectral sequence

Abstract

USING A mod-p version of the lower central series one of us recently [lo] constructed a mod-p version of the spectral sequence of one of the others [3] and showed that for every topological space X there exists a spectral sequence {E’X, d’X) with the following properties: (i) E’X depends only on H,(X; Z,), (ii) for simply connected X the spectral sequence converges in the same sense as the Adams spectral sequence [I]. Our concern here is mainly with a stable version of this sequence, for which we I. explicitly calculate El and d’ II. show that, from E2 on, this stable spectral sequence coincides with the Adams spectral sequence.