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Elementary totally disconnected, locally compact groups of higher complexity (2310.13239v1)
Published 20 Oct 2023 in math.GR
Abstract: The article focuses on a class of second countable groups assembled from profinite and discrete by elementary operations. We focus on a rank associated with these groups that measure their complexity, the decomposition rank. A collection of groups acting on $\aleph_0$-regular trees is defined and used for the first construction of a group with decomposition rank $\omega\omega+1$.