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arXiv · 1107.2590

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

Benno Kuckuck
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Abstract

We analyse the subgroup structure of direct products of groups. Earlier work on this topic has revealed that higher finiteness properties play a crucial role in determining which groups appear as subgroups of direct products of free groups or limit groups. Here, we seek to relate the finiteness properties of a subgroup to the way it is embedded in the ambient 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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Benno Kuckuck. 2011-07-13. Subdirect products of groups and the n-(n+1)-(n+2) Conjecture. https://arxiv.org/abs/1107.2590

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