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Creators/Authors contains: "Osin, Denis"

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  1. (, L’Enseignement Mathématique)
    The goal of this note is to provide yet another proof of the following theorem of Golod: there exists an infinite finitely generated groupGsuch that every element ofGhas finite order. Our proof is based on the Nielsen–Schreier index formula and is simple enough to be included in a standard group theory course. 
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    Free, publicly-accessible full text available February 10, 2026
  2. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract For each prime 𝑝 and each positive integer 𝑑, we construct the first examples of second countable, topologically simple 𝑝-adic Lie groups of dimension 𝑑 whose Lie algebras are abelian.This answers several questions of Glöckner and Caprace–Monod.The proof relies on a generalization of small cancellation methods that applies to central extensions of acylindrically hyperbolic groups. 
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  3. ; ; ; (, Annals of Mathematics)
    We introduce a new class of groups called {\it wreath-like products}. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many wreath-like products have Kazhdan's property (T). In this paper, we prove that any group $$G$$ in a natural family of wreath-like products with property (T) is W$^*$-superrigid: the group von Neumann algebra $$\text{L}(G)$$ remembers the isomorphism class of $$G$$. This allows us to provide the first examples (in fact, $$2^{\aleph_0}$$ pairwise non-isomorphic examples) of W$^*$-superrigid groups with property (T). 
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  4. ; ; ; (, Annals of mathematics)
    Accepted Manuscript Full Text Available
  5. ; ; (, Journal of Topology and Analysis)
    We address the following natural extension problem for group actions: Given a group [Formula: see text], a subgroup [Formula: see text], and an action of [Formula: see text] on a metric space, when is it possible to extend it to an action of the whole group [Formula: see text] on a (possibly different) metric space? When does such an extension preserve interesting properties of the original action of [Formula: see text]? We begin by formalizing this problem and present a construction of an induced action which behaves well when [Formula: see text] is hyperbolically embedded in [Formula: see text]. Moreover, we show that induced actions can be used to characterize hyperbolically embedded subgroups. We also obtain some results for elementary amenable groups. 
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