منابع مشابه
A topological Tits alternative
Let k be a local field, and Γ ≤ GLn(k) a linear group over k. We prove that Γ contains either a relatively open solvable subgroup or a relatively dense free subgroup. This result has applications in dynamics, Riemannian foliations and profinite groups.
متن کاملThe Tits Alternative
We shall say that the Tits Alternative holds for a class of groups if each group in the class is either solvable by ...nite (that is, contains a solvable normal subgroup of ...nite index) or contains a free subgroup of rank at least 2. Free groups of rank 2 contain free subgroups of countable rank, so in the second case there will be of free subgroups of all ...nite ranks. The Tits Alternative ...
متن کاملA Strong Tits Alternative
We show that for every integer d ∈ N, there is N(d) ∈ N such that if K is any field and F is a finite subset of GLd(K), which generates a non amenable subgroup, then F contains two elements, which freely generate a non abelian free subgroup. This improves the original statement of the Tits alternative. It also implies a growth gap and a co-growth gap for non-amenable linear groups, and has cons...
متن کاملDynamic cellular automata: an alternative approach to cellular simulation.
A wide variety of approaches, ranging from Petri nets to systems of partial differential equations, have been used to model very specific aspects of cellular or biochemical functions. Here we describe how an agent-based or dynamic cellular automata (DCA) approach can be used as a very simple, yet very general method to model many different kinds of cellular or biochemical processes. Specificall...
متن کاملTits alternative for 3-manifold groups
Let M be an irreducible, orientable, closed 3-manifold with fundamental group G. We show that if the pro-p completion Ĝp of G is infinite then G is either soluble-by-finite or contains a free subgroup of rank 2.
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2019
ISSN: 1661-7207
DOI: 10.4171/ggd/529