Girth Alternative for HNN Extensions
Azer Akhmedov, Pratyush Mishra
TL;DR
This paper proves the Girth Alternative for a specific class of HNN extensions of finitely generated groups and provides counterexamples showing it does not hold universally.
Contribution
It establishes the Girth Alternative for a new class of HNN extensions and identifies limitations with counterexamples.
Findings
Girth Alternative holds for certain HNN extensions.
Counterexamples show the failure of the Girth Alternative beyond the studied class.
The paper advances understanding of geometric properties of group extensions.
Abstract
We prove the Girth Alternative for a sub-class of the HNN extensions of finitely generated groups. We also produce counterexamples to show that beyond our class, the alternative fails in general.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Finite Group Theory Research