HNN extensions and stackable groups

作者：Hermiller Susan^*; Martinez Perez Conchita

来源：Groups, Geometry, and Dynamics, 2018, 12(3): 1123-1158.

DOI：10.4171/GGD/467

• HNN extension
• algorithms in groups theory
• Dehn function

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 the word problem. In this paper we give two new characterizations 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 similar methods to show that there exist finitely presented metabelian groups that are non-constructible but admit an autostackable structure.

• 出版日期2018