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Author: Roland Schmidt
Publisher: Walter de Gruyter
ISBN: 3110868644
Category : Mathematics
Languages : en
Pages : 589
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Book Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Author: Roland Schmidt
Publisher: Walter de Gruyter
ISBN: 3110868644
Category : Mathematics
Languages : en
Pages : 589
Get Book Here
Book Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Author: Michio Suzuki
Publisher: Springer Science & Business Media
ISBN: 3642527582
Category : Mathematics
Languages : en
Pages : 103
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Book Description
The central theme of this monograph is the relation between the structure of a group and the structure of its lattice of subgroups. Since the first papers on this topic have appeared, notably those of BAER and ORE, a large body of literature has grown up around this theory, and it is our aim to give a picture of the present state of this theory. To obtain a systematic treatment of the subject quite a few unpublished results of the author had to be included. On the other hand, it is natural that we could not reproduce every detail and had to treat some parts some wh at sketchily. We have tried to make this report as self-contained as possible. Accordingly we have given some proofs in considerable detail, though of course it is in the nature of such areport that many proofs have to be omitted or can only be given in outline. Similarly references to the concepts and theorems used are almost exclusively references to standard works like BIRKHOFF [lJ and ZASSENHAUS [lJ. The author would like to express his sincere gratitude to Professors REINHOLD BAER and DONALD G. HIGMAN for their kindness in giving hirn many valuable suggestions. His thanks are also due to Dr. NOBORU ITo who, during stimulating conversations, contributed many useful ideas. Urbana, May, 1956. M. Suzuki. Contents.
Author: Lynne M. Butler
Publisher: American Mathematical Soc.
ISBN: 082182600X
Category : Mathematics
Languages : en
Pages : 173
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Book Description
This work presents foundational research on two approaches to studying subgroup lattices of finite abelian p-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schützenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.
Author: Alexander Lubotzky
Publisher: Birkhäuser
ISBN: 3034889658
Category : Mathematics
Languages : en
Pages : 463
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Book Description
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. 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. 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 p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'.
Author: James E. Karns
Publisher:
ISBN:
Category : Group theory
Languages : en
Pages : 150
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Book Description
Author: Madabusi S. Raghunathan
Publisher: Springer
ISBN: 9783642864285
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book originated from a course of lectures given at Yale University during 1968-69 and a more elaborate one, the next year, at the Tata Institute of Fundamental Research. Its aim is to present a detailed ac count of some of the recent work on the geometric aspects of the theory of discrete subgroups of Lie groups. Our interest, by and large, is in a special class of discrete subgroups of Lie groups, viz., lattices (by a lattice in a locally compact group G, we mean a discrete subgroup H such that the homogeneous space GJ H carries a finite G-invariant measure). It is assumed that the reader has considerable familiarity with Lie groups and algebraic groups. However most of the results used frequently in the book are summarised in "Preliminaries"; this chapter, it is hoped, will be useful as a reference. We now briefly outline the contents of the book. Chapter I deals with results of a general nature on lattices in locally compact groups. The second chapter is an account of the fairly complete study of lattices in nilpotent Lie groups carried out by Ma1cev. Chapters III and IV are devoted to lattices in solvable Lie groups; most of the theorems here are due to Mostow. In Chapter V we prove a density theorem due to Borel: this is the first important result on lattices in semisimple Lie groups.
Author: John Shareshian
Publisher:
ISBN:
Category :
Languages : en
Pages : 360
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Book Description
Author: Gregori A. Margulis
Publisher: Springer Science & Business Media
ISBN: 9783540121794
Category : Mathematics
Languages : en
Pages : 408
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Book Description
Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry. Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete groups is unthinkable. This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. Since the notion of "Lie group" is sufficiently general, the author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature, e.g. classification results on abstract homomorphisms of semi-simple algebraic groups over global fields. The treatise of course contains a presentation of the author's fundamental rigidity and arithmeticity theorems. The work in this monograph requires the language and basic results from fields such as algebraic groups, ergodic theory, the theory of unitary representatons, and the theory of amenable groups. The author develops the necessary material from these subjects; so that, while the book is of obvious importance for researchers working in related areas, it is essentially self-contained and therefore is also of great interest for advanced students.
Author: M.E Anderson
Publisher: Springer Science & Business Media
ISBN: 9400928718
Category : Computers
Languages : en
Pages : 197
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Book Description
The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].
Author: Robert L. Griess
Publisher:
ISBN: 9781571462060
Category : Finite groups
Languages : en
Pages : 0
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Book Description
Rational lattices occur throughout mathematics, as in quadratic forms, sphere packing, Lie theory, and integral representations of finite groups. Studies of high-dimensional lattices typically involve number theory, linear algebra, codes, combinatorics, and groups. This book presents a basic introduction to rational lattices and finite groups and to the deep relationship between these two theories. Robert L. Griess, Jr. is a professor of mathematics at the University of Michigan. His various honors include a Guggenheim Fellowship, an invited lecture at the International Congress of Mathematicians, membership in the American Academy of Arts and Sciences, and the 2010 AMS Leroy P. Steele Prize for his seminal construction of the Monster group. Rational lattices occur throughout mathematics, as in quadratic forms, sphere packing, Lie theory, and integral representations of finite groups. Studies of high-dimensional lattices typically involve number theory, linear algebra, codes, combinatorics, and groups. This book presents a basic introduction to rational lattices and finite groups and to the deep relationship between these two theories. Robert L. Griess, Jr. is a professor of mathematics at the University of Michigan. His various honors include a Guggenheim Fellowship, an invited lecture at the International Congress of Mathematicians, membership in the American Academy of Arts and Sciences, and the 2010 AMS Leroy P. Steele Prize for his seminal construction of the Monster group.|Rational lattices occur throughout mathematics, as in quadratic forms, sphere packing, Lie theory, and integral representations of finite groups. Studies of high-dimensional lattices typically involve number theory, linear algebra, codes, combinatorics, and groups. This book presents a basic introduction to rational lattices and finite groups and to the deep relationship between these two theories. Robert L. Griess, Jr. is a professor of mathematics at the University of Michigan. His various honors include a Guggenheim Fellowship, an invited lecture at the International Congress of Mathematicians, membership in the American Academy of Arts and Sciences, and the 2010 AMS Leroy P. Steele Prize for his seminal construction of the Monster group.|Rational lattices occur throughout mathematics, as in quadratic forms, sphere packing, Lie theory, and integral representations of finite groups. Studies of high-dimensional lattices typically involve number theory, linear algebra, codes, combinatorics, and groups. This book presents a basic introduction to rational lattices and finite groups and to the deep relationship between these two theories. Robert L. Griess, Jr. is a professor of mathematics at the University of Michigan. His various honors include a Guggenheim Fellowship, an invited lecture at the International Congress of Mathematicians, membership in the American Academy of Arts and Sciences, and the 2010 AMS Leroy P. Steele Prize for his seminal construction of the Monster group.
