1,720,975 research outputs found
Acylindrically hyperbolic groups with exotic properties
No full textWe prove that every countable family of countable acylindrically hyperbolic groups has a common finitely generated acylindrically hyperbolic quotient. As an application, we obtain an acylindrically hyperbolic group Q with strong fixed point properties: Q has property FL^p for all p∈[1,+∞),and every action of Q on a finite dimensional contractible topological space has a fixed point. In addition, Q has other properties which are rather unusual for groups exhibiting "hyperbolic-like" behaviour. E.g., Q is not uniformly non-amenable and has finite generating sets with arbitrary large balls consisting of torsion elements
Simple p-adic Lie groups with abelian Lie algebras
No full textFor 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
Fixed subgroups of automorphisms of relatively hyperbolic groups
No full textLet G be a finitely generated relatively hyperbolic group. We show that if no peripheral subgroup of G is hyperbolic relative to a collection of proper subgroups, then the fixed subgroup of every automorphism of G is relatively quasiconvex. It follows that the fixed subgroup is itself relatively hyperbolic with respect to a natural family of peripheral subgroups. If all peripheral subgroups of G are slender (respectively, slender and coherent), our result implies that the fixed subgroup of every automorphism of G is finitely generated (respectively, finitely presented). In particular, this happens when G is a limit group, and thus for any automorphism \phi of G, Fix(\phi) is a limit subgroup of G
Normal automorphisms of relatively hyperbolic groups
No full textAn automorphism of a group G is normal if it fixes every normal subgroup of G setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group G, Inn(G) has finite index in the subgroup Aut_n(G) of normal automorphisms. If, in addition, G is non-elementary and has no non-trivial finite normal subgroups, then Aut_n(G)=Inn(G). As an application, we show that Out(G) is residually finite for every finitely generated residually finite group G with more than one end
Acylindrical hyperbolicity of groups acting on trees
No full textWe provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees. In particular, we consider amalgamated products and HNN-extensions, 1-relator groups, automorphism groups of polynomial algebras, 3-manifold groups and graph products. Acylindrical hyperbolicity is then used to obtain some results about the algebraic structure, analytic properties and measure equivalence rigidity of groups from these classe
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Two projects on equations over generalizations of hyperbolic groups
No full textIn this dissertation, we present the results of two projects, both related to equations over groups and each concerning a particular generalization of hyperbolic groups. Their abstracts are presented below.
A subgroup of a group is called \textit{algebraic} if it can be expressed as a finite union of solution sets to systems of equations. We prove that a non-elementary subgroup of an acylindrically hyperbolic group is algebraic if and only if there exists a finite subgroup of such that . We provide some applications of this result to free products, torsion-free relatively hyperbolic groups, and ascending chains of algebraic subgroups in acylindrically hyperbolic groups.
A group is called \textit{mixed identity-free} if for every and every there exists a homomorphism such that is the identity on and is nontrivial. In this paper, we make a modification to the construction of elementary amenable lacunary hyperbolic groups provided by Ol'shanskii, Osin, and Sapir in their paper \textit{Lacunary hyperbolic groups} to produce finitely generated elementary amenable groups which are mixed identity-free. As a byproduct of this construction, we also obtain locally finite -groups which are mixed identity-free
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
A generalization of the distortion function and the asymptotic geometry of subgroups
No full textThis thesis introduces and studies a natural generalization of the distortion
function that applies to not necessarily finitely generated subgroups of finitely
generated groups. We begin by computing this function in several natural cases,
and provides an example of a group with an uncountable collection of incom-
parably distorted subgroups.We then show that when we restrict this function
to the case of finitely generated subgroups H of finitely generated groups G,
the generalized distortion function characterizes when a natural subspace of the
asymptotic cone of G corresponding to H is connected. We denote this subspace
by Coneω
G(H) and show that the ordinary distortion function is not sufficient to
detect this subspace’s connectedness. We then study the convexity properties
of Coneω
G(H). We show that a subgroup H of a finitely generated group G
is strongly quasi-convex if and only if Coneω
G(H) satisfies a natural convexity
property in Coneω (G). G acts on Coneω (G) in a natural way. We show that the
stabilizer of Coneω
G(G) is the same as the commensurator of H in G whenever
H is strongly quasi-convex in G. We conclude by providing several applications
of this result to groups with Morse elements
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