Finiteness properties of locally defined groups
Daniel S. Farley
Miami University, Oxford, USABruce Hughes
Vanderbilt University, Nashville, USA
![Finiteness properties of locally defined groups cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-jca.png&w=3840&q=90)
Abstract
Let be a set and let be an inverse semigroup of partial bijections of . Thus, an element of is a bijection between two subsets of , and the set is required to be closed under the operations of taking inverses and compositions of functions. We define to be the set of self-bijections of in which each is expressible as a union of finitely many members of . This set is a group with respect to composition. The groups form a class containing numerous widely studied groups, such as Thompson’s group , the Nekrashevych–Röver groups, Houghton’s groups, and the Brin–Thompson groups , among many others. We offer a unified construction of geometric models for and a general framework for studying the finiteness properties of these groups.
Cite this article
Daniel S. Farley, Bruce Hughes, Finiteness properties of locally defined groups. J. Comb. Algebra (2024), published online first
DOI 10.4171/JCA/91