Geodesic
HNN extensions and stackable groups
Susan Hermiller1 ; Conchita Martínez-Pérez2
1University of Nebraska, Lincoln, USA
2Universidad de Zaragoza, Spain
Groups, geometry, and dynamics, Tome 12 (2018) no. 3, pp. 1123-1158

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DOI

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.
DOI : 10.4171/ggd/467
Classification : 20-XX, 68-XX
Mots-clés : HNN extension, algorithms in groups theory, Dehn function

Susan Hermiller  1   ; Conchita Martínez-Pérez  2

1 University of Nebraska, Lincoln, USA
2 Universidad de Zaragoza, Spain 
Susan Hermiller; Conchita Martínez-Pérez. HNN extensions and stackable groups. Groups, geometry, and dynamics, Tome 12 (2018) no. 3, pp. 1123-1158. doi: 10.4171/ggd/467
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     title = {HNN extensions and stackable groups},
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     pages = {1123--1158},
     year = {2018},
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     doi = {10.4171/ggd/467},
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