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Stackability for finitely presented groups consists of a dynamical system that iteratively moves paths into a maximal tree in the Cayley graph. Combining with formal language theoretic restrictions yields auto- or algorithmic stackability, which implies solvability of theword problem. In this paperwe give two newcharacterizations of the stackable property for groups, and use these to show that every HNN extension of a stackable group over finitely generated subgroups is stackable. We apply this to exhibit a wide range of Dehn functions that are admitted by stackable and autostackable groups, as well as an example of a stackable group with unsolvable word problem. We use similarmethods to show that there exist finitely presented metabelian groups that are non-constructible but admit an autostackable structure.
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Susan Hermiller, Conchita Martínez-Pérez, HNN extensions and stackable groups. Groups Geom. Dyn. 12 (2018), no. 3, pp. 1123–1158DOI 10.4171/GGD/467