Homology and Derived p-Series of Groups

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dc.creatorCochran, Tim D.
dc.creatorHarvey, Shelly
dc.date2007-02-28
dc.date2007-04-05
dc.date.accessioned2026-07-07T10:38:20Z
dc.date.available2026-07-07T10:38:20Z
dc.descriptionWe prove that groups that are mod-p-homology equivalent are isomorphic modulo any term of their derived p-series, in precise analogy to Stallings' 1963 result for the lower-central p-series. Similarly spaces that are mod-p-homology equivalent have fundamental groups that are isomorphic modulo any term of their p-derived series. Various authors have related the ranks of the successive quotients of the lower central p-series and of the derived p-series of the fundamental group of a 3-manifold M to the volume of M, to whether certain subgroups of the fundamental group of M are free, whether finite index subgroups of the fundamental group of M map onto non-abelian free groups, and to whether finite covers of M are ``large'' in various other senses. Specifically, let A be a finitely-generated group and B be a finitely presented group. If a homomorphism induces an isomorphism (respectively monomorphism) on H_1(- ;Z_p) and an epimorphism on H_2(- ;Z_p), then for each finite n, it induces an isomorphism (respectively monomorphism) between the quotients of A and B by the n-th terms of their respective p-derived series. In fact we prove a stronger version that is analogous to Dwyer's extension of Stallings' theorem.
dc.description16 pages, simplified some proofs, added references, added a few applications
dc.identifierhttps://arxiv.org/abs/math/0702894
dc.identifierhttp://arxiv.org/abs/math/0702894
dc.identifierJournal London Math. Soc., Vol. 8 part 3(2008)677-692
dc.identifierdoi:10.2140/agt.2008.8.1593
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/180685
dc.subjectGeometric Topology
dc.subjectGroup Theory
dc.subject57M27, 57M07, 20J05 (primary), 55P60 (secondary
dc.titleHomology and Derived p-Series of Groups
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