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• W4300048524 abstract "Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson's group V. Guided by previous work on Thompson's group V, we establish a number of new results about FSS groups. Our main result is that a class of FSS groups are of type F-infinity. This generalizes work of Ken Brown from the 1980s. Next, we develop methods for distinguishing between isomorphism types of some of the Nekrashevych-Rover groups V_{d}(H), where H is a finite group, and show that all such groups V_{d}(H) have simple subgroups of finite index. Lastly, we show that FSS groups defined by small Sim-structures are braided diagram groups over tree-like semigroup presentations. This generalizes a result of Guba and Sapir, who first showed that Thompson's group V is a braided diagram group." @default.
• W4300048524 created "2022-10-03" @default.
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• W4300048524 date "2012-06-12" @default.
• W4300048524 modified "2023-09-29" @default.
• W4300048524 title "Finiteness properties of some groups of local similarities" @default.
• W4300048524 doi "https://doi.org/10.48550/arxiv.1206.2692" @default.
• W4300048524 hasPublicationYear "2012" @default.
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