Algorithms for the Tits alternative and related problems
نویسندگان
چکیده
منابع مشابه
Algorithms for the Tits alternative and related problems
Article history: Received 10 January 2011 Available online 12 August 2011 Communicated by Derek Holt
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Tits has shown that a finitely generated matrix group either contains a nonabelian free group or has a solvable subgroup of finite index. We give a polynomial time algorithm for deciding which of these two conditions holds for a given finitely generated matrix group over an algebraic number field. Noting that many computational problems are undecidable for groups with nonabelian free subgroups,...
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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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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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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.06.036