Displaying similar documents to “The Bass conjecture and growth in groups”

The Ore conjecture

Martin Liebeck, E.A. O’Brien, Aner Shalev, Pham Tiep (2010)

Journal of the European Mathematical Society

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The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remains open for various infinite families of simple groups. In this paper we develop new strategies, combining character-theoretic methods with other ingredients, and use them to establish the conjecture.

Remarks on Yu’s ‘property A’ for discrete metric spaces and groups

Jean-Louis Tu (2001)

Bulletin de la Société Mathématique de France

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Guoliang Yu has introduced a property on discrete metric spaces and groups, which is a weak form of amenability and which has important applications to the Novikov conjecture and the coarse Baum–Connes conjecture. The aim of the present paper is to prove that property in particular examples, like spaces with subexponential growth, amalgamated free products of discrete groups having property A and HNN extensions of discrete groups having property A.

On Brauer’s Height Zero Conjecture

Gabriel Navarro, Britta Späth (2014)

Journal of the European Mathematical Society

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In this paper, the unproven half of Richard Brauer’s Height Zero Conjecture is reduced to a question on simple groups.

Differential analogues of the Brück conjecture

Xiao-Guang Qi, Lian-Zhong Yang (2011)

Annales Polonici Mathematici

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We give some growth properties for solutions of linear complex differential equations which are closely related to the Brück Conjecture. We also prove that the Brück Conjecture holds when certain proximity functions are relatively small.

Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics

Tatiana Bandman, Shelly Garion, Boris Kunyavskiĭ (2014)

Open Mathematics

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We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.

On the exponent of the cokernel of the forget-control map on K₀-groups

Francis X. Connolly, Stratos Prassidis (2002)

Fundamenta Mathematicae

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For groups that satisfy the Isomorphism Conjecture in lower K-theory, we show that the cokernel of the forget-control K₀-groups is composed by the NK₀-groups of the finite subgroups. Using this information, we can calculate the exponent of each element in the cokernel in terms of the torsion of the group.

On groups with linear sci growth

Louis Funar, Martha Giannoudovardi, Daniele Ettore Otera (2015)

Fundamenta Mathematicae

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We prove that the semistability growth of hyperbolic groups is linear, which implies that hyperbolic groups which are sci (simply connected at infinity) have linear sci growth. Based on the linearity of the end-depth of finitely presented groups we show that the linear sci is preserved under amalgamated products over finitely generated one-ended groups. Eventually one proves that most non-uniform lattices have linear sci.