Lubotzky, Alexander 1956Overview
Publication Timeline
Most widely held works by
Alexander Lubotzky
Discrete groups, expanding graphs and invariant measures
by Alexander Lubotzky
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25 editions published between 1994 and 2010 in English and held by 739 WorldCat member libraries worldwide Presents the solutions to two problems: the first is the construction of expanding graphs  graphs which are of fundamental importance for communication networks and computer science, and the second is the Ruziewicz problem concerning the finitely additive invariant measures on spheres
Tree lattices
by Hyman Bass
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10 editions published between 2000 and 2001 in English and held by 300 WorldCat member libraries worldwide Group actions on trees furnish a unified geometric way of recasting the chapter of combinatorial group theory dealing with free groups, amalgams, and HNN extensions. Some of the principal examples arise from rank one simple Lie groups over a nonarchimedean local field acting on their BruhatTits trees. In particular this leads to a powerful method for studying lattices in such Lie groups. This monograph extends this approach to the more general investigation of Xlattices G, where Xis a locally finite tree and G is a discrete group of automorphisms of X of finite covolume. These "tree lattices" are the main object of study. Special attention is given to both parallels and contrasts with the case of Lie groups. Beyond the Lie group connection, the theory has application to combinatorics and number theory. The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of nonuniform tree lattices, including some fundamental and recently proved existence theorems. Nonuniform tree lattices are much more complicated than uniform ones; thus a good deal of attention is given to the construction and study of diverse examples. The fundamental technique is the encoding of tree action in terms of the corresponding quotient "graphs of groups." Tree Lattices should be a helpful resource to researcher sin the field, and may also be used for a graduate course on geometric methods in group theory
Subgroup growth
by Alexander Lubotzky
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Book
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9 editions published between 2003 and 2004 in English and held by 259 WorldCat member libraries worldwide Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible "growth types", for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. For example the socalled PSG Theorem, proved in Chapter 5, characterizes the groups of polynomial subgroup growth as those which are virtually soluble of finite rank. A key element in the proof is the growth of congruence subgroups in arithmetic groups, a new kind of "noncommutative arithmetic", with applications to the study of lattices in Lie groups. Another kind of noncommutative arithmetic arises with the introduction of subgroupcounting zeta functions; these fascinating and mysterious zeta functions have remarkable applications both to the "arithmetic of subgroup growth" and to the classification of finite pgroups. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and strong approximation, algebraic and analytic number theory, probability, and padic model theory. Relevant aspects of such topics are explained in selfcontained "windows", making the book accessible to a wide mathematical readership. The book concludes with over 60 challenging open problems that will stimulate further research in this rapidly growing subject
Varieties of representations of finitely generated groups
by Alexander Lubotzky
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Book
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10 editions published in 1985 in English and held by 228 WorldCat member libraries worldwide
The word and riemannian metrics on lattices of semisimple groups
by Alexander Lubotzky
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3 editions published between 2000 and 2001 in English and held by 13 WorldCat member libraries worldwide
Subgroup growth
by Alexander Lubotzky
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2 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
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1 edition published in 1979 in Hebrew and held by 2 WorldCat member libraries worldwide
Rekonstruktion und relative Chronologie : Akten der VIII. Fachtagung der Indogermanischen Gesellschaft, Leiden, 31. August4. September 1987
by Fachtagung der Indogermanischen Gesellschaft
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1 edition published in 1992 in German and held by 2 WorldCat member libraries worldwide
Discrete groups, expanding graphs and invariant measures : preliminary version
by Alexander Lubotzky
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Book
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1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
Beauville surfaces and finite simple groups
by Shelly Garion
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1 edition published in 2010 in English and held by 1 WorldCat member library worldwide A Beauville surface is a rigid complex surface of the form (C1 × C2)/G, where C1 and C2 are nonsingular, projective, higher genus curves, and G is a finite group acting freely on the product. Bauer, Catanese, and Grunewald conjectured that every finite simple group G, with the exception of A5, gives rise to such a surface. We prove that this is so for almost all finite simple groups (i.e., with at most finitely many exceptions). The proof makes use of the structure theory of finite simple groups, probability theory, and character estimates Audience Level
Related Identities
Associated Subjects
Algebra Algebraic varieties Combinatorial analysis Discrete groups Finite groups Geometry, Differential Global differential geometry Graph theory Group schemes (Mathematics) Group theory IndoEuropean languages Infinite groups Invariant measures Lfunctions Lie groups Mathematics Number theory Reconstruction (Linguistics) Representations of groups Subgroup growth (Mathematics) Topological groups Trees (Graph theory)

Alternative Names
Lubotzky, A. 1956
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