Free subgroups in linear groups

DOI10.1016/0021-8693(72)90058-0zbMath0236.20032OpenAlexW2040034546WikidataQ55954586 ScholiaQ55954586MaRDI QIDQ2552199

Publication date: 1972

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(72)90058-0

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15)

Related Items

On random walks on wreath products, Uniform Kazhdan constants and paradoxes of the affine plane, Finite dimensional groups of local diffeomorphisms, Strong Tits alternatives for compact 3-manifolds with boundary, Maximal subgroups of almost subnormal subgroups in division rings, About affine Anosov diffeomorphisms with differentiable stable and instable foliations, Mapping class groups and outer automorphism groups of free groups are $C^{*}$-simple, Word maps have large image., A faithful linear-categorical action of the mapping class group of a surface with boundary, Ping-pong groups and counting functions, Lorentz spacetimes of constant curvature, Groups acting on CAT(0) square complexes, Semigroups containing proximal linear maps, Generalised Tits alternative for linear semigroups, Fixed points and amenability in non-positive curvature, Almost Engel linear groups, Schottky groups and maximal representations, The linearity of automorphism groups of relatively free groups, Orbihedra of nonpositive curvature, Duality of the Kulkarni limit set for subgroups of $\mathrm {PSL}(3,\mathbb {C})$, Asymptotic behavior of the Riemannian Heisenberg group and its horoboundary, Topological generation of exceptional algebraic groups, Interval exchanges that do not occur in free groups, Strongly dense free subgroups of semisimple algebraic groups., Maximal subgroups of $\mathrm{SL}_{n}(D)$, First order rigidity of non-uniform higher rank arithmetic groups, Right-angled Artin groups and a generalized isomorphism problem for finitely generated subgroups of mapping class groups, The conjugacy problem in automaton groups is not solvable., Large deviation principle for random matrix products, Non-abelian tensor product of residually finite groups, On the groups of unitriangular automorphisms of relatively free groups., Generic-case complexity, decision problems in group theory, and random walks., Characterization of the soluble radical by a sequence of words., Cryptosystems using linear groups, Revisiting the Siegel upper half plane. I., Profinite groups with a cyclotomic $p$-orientation, Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics., Tits alternative for maximal subgroups of $\text{GL}_n(D)$., Tits alternative for closed real analytic 4-manifolds of nonpositive curvature., Kesten's theorem for invariant random subgroups., Transience of algebraic varieties in linear groups -- applications to generic Zariski density., Not residually finite groups of intermediate growth, commensurability and non-geometricity., On locally finite skew group algebras, Linear algebraic groups with good reduction, PI-groups and PI-representations of groups., Finitely generated profinitely dense free groups in higher rank semi-simple groups, On problems related to growth, entropy, and spectrum in group theory, Heights in families of abelian varieties and the geometric Bogomolov conjecture, Discriminant complements and kernels of monodromy representations, Tits topology and fundamental groups of compact Riemannian manifolds, Amenability, bi-Lipschitz equivalence, and the von Neumann conjecture, Free $^*$-subalgebras of C$^*$-algebras, Tits alternative for groups acting properly on 2-dimensional recurrent complexes, Groups of fast homeomorphisms of the interval and the ping-pong argument, Outer automorphism groups of graph products: subgroups and quotients, Obstructions to matricial stability of discrete groups and almost flat $K$-theory, Bounded Engel elements in groups satisfying an identity, Discriminants and automorphism groups of Veronese subrings of skew polynomial rings, Evaluation of circuits over nilpotent and polycyclic groups, Some new parallels between groups and Lie algebras, or what can be simpler than multiplication table?, Finitary random interlacements and the Gaboriau-Lyons problem, Positive laws on word values in residually-$p$ groups., On profinite groups with Engel-like conditions., Groups with a positive law on commutators., Algebraic entropy of elementary amenable groups., On uniform exponential growth for linear groups., Incoherence of integral group rings., Abelian subgroup structure of square complex groups and arithmetic of quaternions, A combination theorem for Anosov subgroups, Bounded Engel elements in residually finite groups, New Zémor-Tillich type hash functions over $\mathrm{GL}_2 (\mathbb{F}_{p^n})$, Non virtually solvable subgroups of mapping class groups have non virtually solvable representations, On the Burau representation of B4, Growth of periodic Grigorchuk groups, On the Tits alternative for $PD(3)$ groups, Linear groups and computation, A sharper Tits alternative for 3-manifold groups, Growth of homogeneous spaces, density of discrete subgroups and Kazhdan's property $(T)$, Some groups whose reduced $C^*$-algebra is simple, The automorphism group and limit set of a bounded domain I: the finite type case, Zariski dense subgroups of arithmetic groups, Most big mapping class groups fail the Tits alternative, Distortion of distances in $p$-adic groups, Conjugacy classes of n-tuples in Lie algebras and algebraic groups, Reduction theorems for groups of matrices, Nilpotence of orbits under monodromy and the length of Melnikov functions, The congruence topology, Grothendieck duality and thin groups, Invariant analytic hypersurfaces, Representation varieties and character varieties, New combinatorial properties of linear groups, Free products of units in algebras. II: Crossed products, Exponential radicals of solvable Lie groups, Chain conditions for subgroups of infinite order or index, On units of twisted group algebras, An alternative for minimal group actions on totally regular curves, The linear part of a discontinuously acting Euclidean semigroup, The dynamics of solvable subgroups of $\text{PSL}(3,\mathbb{C})$, Extensions and isomorphisms for the generalized Fourier algebras of a locally compact group, On dense free subgroups of Lie groups, Invariant random subgroups of linear groups, Automorphisms of algebraic varieties and infinite transitivity, List of problems on discrete subgroups of Lie groups and their computational aspects, A hyperbolic lattice in each dimension with Zariski-dense surface subgroups, Tits-type alternative for certain groups acting on algebraic surfaces, Compactness and Finiteness Results for Gromov-Hyperbolic Spaces, Tits Alternative for -dimensional complexes, Numerical upper bounds on growth of automaton groups, Translation lengths of outer automorphisms of finitely generated free-by-finite groups, Unnamed Item, Automorphism groups of compact complex surfaces: T-Jordan property, Tits alternative and solvability, Free subgroups in almost subnormal subgroups of general skew linear groups, Anosov groups: local mixing, counting and equidistribution, Polynomial growth and subgroups of $\mathrm{Out}(F_N)$, EDT0L grammars with only one variable have tractable generating functions, Thin right‐angled Coxeter groups in some uniform arithmetic lattices, Relativizing characterizations of Anosov subgroups. I (with an appendix by Gregory A. Soifer), On amenability and measure of maximal entropy for semigroups of rational maps: II, Free unit groups in group rings and division rings: My collaboration with Don Passman, Linearity and nonlinearity of groups of polynomial automorphisms of the plane, Construction and applications of proximal maps for typical cocycles, A NOTE ON SUBNORMAL SUBGROUPS IN DIVISION RINGS CONTAINING SOLVABLE SUBGROUPS, Klein-Maskit combination theorem for Anosov subgroups: free products, Spectral gap property and strong ergodicity for groups of affine transformations of solenoids, The rates of growth in a hyperbolic group, REPRESENTATIONS OF BRAID GROUPS VIA CONJUGATION ACTIONS ON CONGRUENCE SUBGROUPS, Narrow normal subgroups of Coxeter groups and of automorphism groups of Coxeter groups, Groups with cofinite Zariski topology and potential density, Permutable subgroups in $\mathrm{GL}_n (D)$ and applications to locally finite group algebras, North-South type dynamics of relative atoroidal automorphisms of free groups on a relative space of currents, Stationary $C^\ast $-dynamical systems (with an appendix by Uri Bader, Yair Hartman, and Mehrdad Kalantar), Horospherical invariant measures and a rank dichotomy for Anosov groups, Flexible stability and nonsoficity, Locally solvable maximal subgroups in division rings, When amenable groups have real rank zero C∗-algebras, Asymptotic behaviors of random walks on countable groups, Discrete groups of packed, non-positively curved, Gromov hyperbolic metric spaces, Unnamed Item, A characterization of growth in locally compact groups, Free subgroups in maximal subgroups of skew linear groups, TORSION-FREE GROUPS WITH RANK RESTRICTING PROPERTIES, Automorphism groups of positive entropy on projective threefolds, Free subgroups in maximal subgroups of SLn(D), Relatively free semigroups of intermediate growth, Linear actions of free groups, Linear groups, Groups of piecewise projective homeomorphisms, On the Gap Conjecture concerning group growth, The word and Riemannian metrics on lattices of semisimple groups, Free subgroups in maximal subgroups of $\text{GL}_1(D)$, A Note on Groups of Intermediate Growth, The Tits Alternative for Tsaranov's Generalized Tetrahedron Groups, Unitary units in group algebras, Unnamed Item, Free unit groups in group algebras, Isometry types of profinite groups., Antifinitary linear groups, A residual property of free groups, Super-rigidity and non-linearity for lattices in products, On free subsemigroups of associative algebras, Convolution of discrete measures on linear groups, The Tits alternative for generalized tetrahedron groups, Convolution of discrete measures on linear groups, Some applications of algebraic entropy to the proof of Milnor-Wolf theorem, Free subgroups in maximal subgroups ofGL_n(D), Lattices in amenable groups, $3$-Manifold Groups are Virtually Residually $p$, Embedding groups in locally (soluble-by-finite) simple groups, A NON-COMMUTATIVITY STATEMENT FOR ALGEBRAIC QUATERNIONS, ОБ АМЕНАБЕЛЬНЫХ ПОДГРУППАХ F-ГРУПП, Bounded Engel elements in residually finite groups satisfying an identity, Nilpotent endomorphisms of expansive group actions, The joint spectrum, Multiplication of weak equivalence classes may be discontinuous, Automorphisms of solvable groups, Growth in groups: ideas and perspectives, Expansions of the real field by discrete subgroups of 𝐺𝑙_{𝑛}(ℂ), Rational growth in torus bundle groups of odd trace, Are there free groups in division rings?, How smooth is quantum complexity?, Subgroups of elliptic elements of the Cremona group, A class of free rotation groups, On solvable subgroups of the Cremona group, Free subgroups in linear groups over some skew fields, The automorphism group of a finitely generated virtually abelian group., Transitive linear groups and nearfields with solubility conditions, Self-similar groups, automatic sequences, and unitriangular representations, Amenable actions and dense subgroups of Lie groups, Quantoren-Elimination bei Fastkörpern. (Elimination of quantifiers in nearfields), Affine linear sieve, expanders, and sum-product, On the growth of $p$-class groups in $p$-class field towers, A spectral gap theorem in simple Lie groups, Piecewise automatic groups., Proper affine actions on semisimple Lie algebras, Almost convergence and its applications to the Fourier-Stieltjes localization, The surgery L-groups of poly-(finite or cyclic) groups, On the Haagerup inequality and groups acting on $\tilde A_ n$-buildings, The Burau representation of the braid group is pairwise free, The growth of linear groups, Compact quotients of non-Archimedean rank-one groups, On degrees of growth of finitely generated groups., A note on the existence of non-cyclic free subgroups in division rings., Semigroups of matrices of intermediate growth., Free subgroups acting properly discontinuously., A finitary version of Gromov's polynomial growth theorem., Group completions and limit sets of Kleinian groups, Polycyclic Frattini factors in certain finitely generated groups, Amenable subgroups of semi-simple groups and proximal flows, Matrix representation for the braid group $B_4$, A simple proof of Borel's density theorem, Book review of: J. Tits, Œuvres. Collected works. Vols. I--IV. Edited by Francis Buekenhout et al., Expansion in $\text{SL}_d(\mathbb Z/q\mathbb Z)$, $q$ arbitrary., The growth functions of finitely generated semigroups, A system of generators in the group of diffeomorphisms of the n- dimensional torus, Maximal subgroups of infinite index in finitely generated linear groups, Free subgroups of dendrite homeomorphism group, The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant, A note on free subgroups in linear groups, On free subgroups of generalized triangle groups, The uses of 2 by 2 matrices in combinatorial group theory. A survey, A height gap theorem for finite subsets of $\mathrm{GL}_{d}(\overline{\mathbb{Q}})$ and nonamenable subgroups, Groups of polynomial growth and expanding maps. Appendix by Jacques Tits, On the linearity of automorphism groups of free groups, Invariant meromorphic functions on complex semisimple Lie groups, Axial isometries of manifolds of non-positive curvature, Instability of nondiscrete free subgroups in Lie groups, Random subgroups of linear groups are free., Free quotients and the congruence kernel of $SL_ 2$., On normal subgroups of multiplicative group of skew fields generated by a polycyclic-by-finite group, On groups of polynomial subgroup growth, The complexity of Grigorchuk groups with application to cryptography, Old and new categorical invariants of manifolds, An obstruction to $\ell^p$-dimension, Uniform independence in linear groups., Commutator length of finitely generated linear groups., An approach to automorphisms of free groups and braids via transvections, Harmonic functions of linear growth on solvable groups, $C^*$-simplicity and the unique trace property for discrete groups, Recurrent orbits of subgroups of local complex analytic diffeomorphisms, The coarse geometry of Hartnell's firefighter problem on infinite graphs, The ubiquity of free groups, The non-abelian tensor square of residually finite groups, Operator ultra-amenability, The girth of convergence groups and mapping class groups., Automorphisms of groups, Hyperbolic configurations of roots and Hecke algebras, The soluble subgroups and the Tits alternative in linear groups over rings of fractions of polycyclic group rings. I, Proper affine actions and geodesic flows of hyperbolic surfaces, Über die Gelfand-Kirillov-Dimension. (On the Gelfand-Kirillov-dimension), A spectral gap theorem in SU$(d)$, On the conjugacy growth functions of groups., Approximate subgroups of linear groups., Local rigidity of discrete groups acting on complex hyperbolic space, On fundamental groups of complete affinely flat manifolds, Embedding some interlacings in groups of automorphisms of finitely generated solvable groups, On finitely generated groups with many profinite-closed subgroups, On the linearity of automorphism groups for free metabelian groups., Transversely homogeneous foliations, Fundamental domains for properly discontinuous affine groups, On the spectrum of the sum of generators for a finitely generated group, Simplicity and superrigidity of twin building lattices., Grothendieck's problem on profinite completions and representations of groups, Tychonoff property for linear groups, Asymptotic growth of finite groups, A theorem of Tits type for compact Kähler manifolds, Algorithms for the Tits alternative and related problems., Free products of units in algebras. I: Quaternion algebras, Algorithms for matrix groups and the Tits alternative, A Tits alternative for groups that are residually of bounded rank, Milnor's alternative for finitely generated relatively free groups that are locally graded, Tits alternative for Artin groups of type FC, The central limit problem on locally compact groups, A theorem of Tits type for automorphism groups of projective varieties in arbitrary characteristic. With an appendix by Tomohide Terasoma, Maximal subgroups of $\text{GL}_1(D)$, Gromov's theorem on groups of polynomial growth and elementary logic, Fixed sets and free subgroups of groups acting on metric spaces, Intertwined mappings, Invariant subspaces of affine groups - An algebraic version of a theorem of Bieberbach, Group rings with solvable unit groups, LOWER BOUNDS ON THE GROWTH OF A GROUP ACTING ON THE BINARY ROOTED TREE, Invariant analytic hypersurfaces in complex Lie groups, Groups with identities, Unnamed Item, Unnamed Item, Freudenthal-Weil theorem for pro-Lie groups, Exponential growth rates of free and amalgamated products., On the growth of a Coxeter group, Milnor Property in Finitely Generated Soluble Groups, Properly discontinuous group actions on affine homogeneous spaces, A Survey on Free Objects in Division Rings and in Division Rings with an Involution, On the Growth of Noetherian Filtered Rings, Some free groups of matrices and the Burau representation of B₄, Unnamed Item, ON THE GROWTH OF HOLOMORPHIC PROJECTIVE FOLIATIONS, Groups with finitely many isomorphic classes of non-abelian subgroups, Free Subgroups of Normal Subgroups of the Multiplicative Group of Skew Fields, On the parallel complexity of linear groups, Polynomials on Affine Manifolds, Groups, nonadditive entropy and phase transitions, Le phénomène de la moyennabilité, Existence of Nonabelian Free Subgroups in the Maximal Subgroups of GL_n(D), Growth rate of cluster algebras, Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint., Produits de matrices aléatoires et applications aux propriétés géometriques des sous-groupes du groupe linéaire, Construction of open sets of free K-tuples of matrices, Multiplicative subgroups in weakly locally finite division rings, Soluble and linear repetitive groups, Free representations of outer automorphism groups of free products via characteristic abelian coverings, Invariant measures of groups of homeomorphisms and Auslander's conjecture, Dimension of character varieties for $3$-manifolds, Conjugacy in polycyclic groups, Free Groups in Central Simple Algebras without Tits' Theorem, On the Tits alternative for a class of finitely presented groups with a special focus on symbolic computations, About the Domino Problem for Subshifts on Groups, Amenability of Groups and G-Sets, Conjugacy in polycyclic groups, Centers of subgroups of big mapping class groups and the Tits alternative, On profinite groups in which commutators are Engel, Orbit decidability and the conjugacy problem for some extensions of groups, Sous-groupes $H$-loxodromiques, EMBEDDING ℤ² * Z AS A DISCRETE SUBGROUP INTO SMALL LINEAR GROUPS, Some matrix groups over finite-dimensional division algebras, On conjugacy growth of linear groups, On Invariant Finitely Additive Measures for Automorphism Groups Acting on Tori, ON GROUPS ADMITTING A WORD WHOSE VALUES ARE ENGEL, Compactifications équivariantes par des courbes, Non-amenable finitely presented torsion-by-cyclic groups, Tits Alternative for Maximal Subgroups of Skew Linear Groups, Measure conjugacy invariants for actions of countable sofic groups, A new proof of Gromov’s theorem on groups of polynomial growth, Embedding free Burnside groups in finitely presented groups., A SURVEY ON FREE SUBGROUPS IN THE GROUP OF UNITS OF GROUP RINGS, Automorphism groufs and subgroups of sl₂over division rings, Bounded Harmonic Functions on Coverings, The Tits Alternative for Spherical Generalized Tetrahedron Groups, FREE SYMMETRIC AND UNITARY PAIRS IN DIVISION RINGS WITH INVOLUTION, Solvable-by-finite subgroups of GL(2, F), Groups rings: an annotated questionnaire, A new measure of growth for groups and algebras, Sieving and expanders, A Residual Property of Certain Linear Groups, Free Subgroups of Groups with Nontrivial Floyd Boundary, Random subgroups of Lie groups, Weak Maximality Condition and Polycyclic Groups, Locally Graded Quotients of Locally Graded Groups, Amenability: A survey for statistical applications of hunt-stein and related conditions on groups, On a Problem of Magnus, Arithmetic hyperbolic reflection groups, Linear Groups with Almost Right Engel Elements, On Residually Finite Groups with Engel-like Conditions, Abstract homomorphisms of algebraic groups: problems and bibliography, Milnor identities, Unnamed Item, Discrete subgroups of the special linear group with thin limit sets, FREE GROUPS OF QUATERNIONS, Integral group rings whose group of units is solvable an elementary proof, Isometry groups of non-positively curved spaces: discrete subgroups, Free products in mapping class groups generated by Dehn twists, Simultaneous Ping-Pong Partners inPSL_n(ℤ), Expander graphs in pure and applied mathematics, Free k-tuples in linear groups, Liouvillian integration and Bernoulli foliations, ON GROUPS WITH TWO ISOMORPHISM CLASSES OF DERIVED SUBGROUPS, Completely bounded homomorphisms of the Fourier algebras, Nonabelian free subgroups in homomorphic images of valued quaternion division algebras, Compactly Generated Subgroups and Open Subgroups of Locally Compact Groups, CHARACTERIZATION OF SOLVABLE GROUPS AND SOLVABLE RADICAL, Generations for arithmetic groups., Polycyclic groups and topology, Complex analytic geometry of complex parallelizable manifolds, Semigroup identities on units of integral group rings, Linear groups and group rings., Group-theoretic compactification of Bruhat–Tits buildings, On Subgroups of the Multiplicative Group of Skew Fields, On residually finite groups in which commutators are engel, Elementary proof of a theorem of Bruhat-Tits-Rousseau and of a theorem of Tits, Varieties and simple groups, Locally Finite Conditions on Maximal Subgroups of GL_n(D)

Cites Work