Free Subgroups of Linear Groups
نویسندگان
چکیده
منابع مشابه
Linear programming and the intersection of subgroups in free groups
We study the intersection of finitely generated subgroups of free groups by utilizing the method of linear programming. We prove that if H1 is a finitely generated subgroup of a free group F , then the Walter Neumann coefficient σ(H1) of H1 is rational and can be computed in deterministic exponential time of size of H1. This coefficient σ(H1) is a minimal nonnegative real number such that, for ...
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This paper is an extension of the talk I gave at the International Conference on Non-Commutative Rings, Group Rings, Diagram Algebras and Applications at the University of Madras in December 2006. It discusses certain techniques used to prove the existence of free subgroups in linear groups and in the unit group of integral group rings of finite groups. Its main focus is recent joint work with ...
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In 1954 A. G. Howson proved that the intersection of two finitely generated subgroups of a free group is again finitely generated. Now the free metabelian subgroups of a free metabelian group of finite rank n are quite restricted. Indeed they are again of finite rank at most n. This suggests that there may be an analog of Howson’s theorem for free metabelian groups. This turns out not to be the...
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The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though...
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For the free topological group on an interval [a, b] a family of closed, locally path-connected subgroups is given such that each group is not projective and so not free topological. Simplicial methods are used, and the test for nonprojectivity is nonfreeness of the group of path components. Similar results are given for the abelian case. Introduction. Let F(X) be the free topological group on ...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2007
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2007.v3.n4.a6