The BNS invariants of the generalized solvable Baumslag-Solitar groups and of their finite index subgroups

2021/10/28 by Sgobbi, Wagner, Wong, Peter
#20F65 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2110.14834

Abstract

We compute the Bieri-Neumann-Strebel invariants Σ¹ for the generalized solvable Baumslag-Solitar groups Γ_n and their finite index subgroups. Using Σ¹, we show that certain finite index subgroups of Γ_n cannot be isomorphic to Γ_k for any k. In addition, we use the BNS-invariants to give a new proof of property R_∞ for the groups Γ_n and their finite index subgroups.

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