Subdirect products of groups and the n-(n+1)-(n+2) theorem

Details Subdirect products of groups and the n-(n+1)-(n+2) theorem Subdirect products of groups and the n-(n+1)-(n+2) theorem

2011-07-13

arxiv.org/abs/1107.2590v1

Mathematics

Group Theory

24 pages

Scientific paper

We analyse the subgroup structure of direct products of groups. In particular, we seek to relate the finiteness properties of a group to the ways in which it embeds non-trivially into a direct product. To this end we formulate a conjecture on finiteness properties of fibre products of groups. We present different approaches to this conjecture, proving a general result on finite generation of homology groups of fibre products and, for certain special cases, results on the stronger finiteness properties F_n and FP_n.

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