Tits alternative for maximal subgroups of GLn(D)
نویسندگان
چکیده
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.
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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 ...
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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...
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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.
متن کاملThe Tits alternative for generalised tetrahedron groups
A generalised tetrahedron group is the colimit of a triangle of groups whose vertex groups are generalised triangle groups and whose edge groups are finite cyclic. We prove an improved Spelling Theorem for generalised triangle groups which enables us to compute the precise Gersten-Stallings angles of this triangle of groups, and hence obtain a classification of generalised tetrahedron groups ac...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2003.09.028