Coherence for elementary amenable groups
Sam Hughes, Dawid Kielak, Peter H. Kropholler, Ian J. Leary
TL;DR
This paper establishes the equivalence of several coherence properties for elementary amenable groups, extending known results from finitely generated soluble groups to a broader class.
Contribution
It generalizes the equivalence of group coherence, homological coherence, and ring coherence from finitely generated soluble groups to elementary amenable groups.
Findings
Coherence, homological coherence, and ring coherence are equivalent for elementary amenable groups.
Generalizes Bieri and Strebel's result to a wider class of groups.
Provides a unified understanding of coherence properties in group theory.
Abstract
We prove that for an elementary amenable group, coherence of the group, homological coherence of the group, and coherence of the integral group ring are all equivalent. This generalises a result of Bieri and Strebel for finitely generated soluble groups.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research