Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homology and Derived p-Series of Groups   We 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.

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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin