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arXiv · 1603.06804

Subgroup graph methods for presentations of finitely generated groups and the connectivity of associated simplicial complexes

Cora Welsch
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Abstract

In this article we generalize the theory of subgroup graphs of subgroups of free groups to finite index subgroups $H$ of finitely generated groups $G$. We study and prove various properties of $H$ in relation to its subgroup graph $\Gamma(H)$. For a finitely generated group $G$ we consider the poset $P_{\text{fi}}(G)$ of all right cosets of all proper finite index subgroups of $G$. We use the theory of subgroup graphs to prove that for many finitely generated infinite groups the order complex $\Delta P_{\text{fi}} (G)$ and the corresponding nerve complex are contractible.

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Cora Welsch. 2016-03-22. Subgroup graph methods for presentations of finitely generated groups and the connectivity of associated simplicial complexes. https://arxiv.org/abs/1603.06804

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