Cohomological finiteness conditions for a class of metabelian groups

TL;DR

This paper investigates a specific class of metabelian groups and demonstrates their alignment with the Bieri-Groves conjecture, linking cohomological finiteness conditions to the Bieri-Neumann-Strebel sigma invariant.

Contribution

It establishes that these groups satisfy the cohomological finiteness conditions predicted by the Bieri-Groves conjecture, extending understanding of their algebraic properties.

Findings

Groups are consistent with the Bieri-Groves conjecture

Links cohomological finiteness to the sigma invariant

Supports conjecture in the context of specific metabelian groups

Abstract

We consider a class of metabelian groups first studied by Baumslag and Stammbach and we show that these groups are consistent with the Bieri-Groves conjecture which relates cohomological finiteness conditions to the Bieri-Neumann-Strebel sigma invariant.