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Large groups, Property (tau) and the homology growth of subgroups

Abstract:

We investigate the homology of finite index subgroups G_i of a given finitely presented group G. Specifically, we examine d_p(G_i), which is the dimension of the first homology of G_i, with mod p coefficients. We say that a collection of finite index subgroups {G_i} has linear growth of mod p homology if the infimum of d_p(G_i)/[G:G_i] is positive. We show that if this holds and each G_i is normal in its predecessor and has index a power of p, then one of the following possibilities must be t...

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Publication status:
Published

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Publisher copy:
10.1017/S0305004108002089

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
Volume:
146
Issue:
3
Pages:
625-648
Publication date:
2005-09-02
DOI:
EISSN:
1469-8064
ISSN:
0305-0041
URN:
uuid:34a45276-c60a-42f8-9ac5-399a185d17a4
Source identifiers:
27445
Local pid:
pubs:27445
Language:
English
Keywords:

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