We prove that groups that are Zp-homology equivalent are isomorphic modulo any term of their derived p-series, in precise analogy to Stallings’ 1963 result for the p−lower-central series. In fact we prove a stronger theorem that is analogous to Dwyer’s extensions of Stallings’ results. Similarly, spaces that are Zp-homology equivalent have isomorphic fundamental groups modulo any term of their ...

The lower central series of a right-angled Coxeter group $$\mathrm{RC}_{\mathcal K}$$ and the corresponding graded Lie algebra $$L(\mathrm{RC}_{\mathcal K})$$ associated with are studied. Relations obtained in components . A basis fourth component for groups at most four generators is described.

Let A be a complex hyperplane arrangement, with fundamental group G and holonomy Lie algebra H. Suppose H3 is a free abelian group of minimum possible rank, given the values the Möbius function μ : L2 → Z takes on the rank 2 flats of A. Then the associated graded Lie algebra of G decomposes (in degrees ≥ 2) as a direct product of free Lie algebras. In particular, the ranks of the lower central ...