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  • 1
    Online Resource
    Online Resource
    Cambridge :Cambridge University Press,
    UID:
    almahu_9948233726102882
    Format: 1 online resource (ix, 199 pages) : , digital, PDF file(s).
    ISBN: 9781139095129 (ebook)
    Series Statement: London Mathematical Society lecture note series ; 395
    Content: Growth of groups is an innovative new branch of group theory. This is the first book to introduce the subject from scratch. It begins with basic definitions and culminates in the seminal results of Gromov and Grigorchuk and more. The proof of Gromov's theorem on groups of polynomial growth is given in full, with the theory of asymptotic cones developed on the way. Grigorchuk's first and general groups are described, as well as the proof that they have intermediate growth, with explicit bounds, and their relationship to automorphisms of regular trees and finite automata. Also discussed are generating functions, groups of polynomial growth of low degrees, infinitely generated groups of local polynomial growth, the relation of intermediate growth to amenability and residual finiteness, and conjugacy class growth. This book is valuable reading for researchers, from graduate students onward, working in contemporary group theory.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Introduction , Some Group Theory , Finite Index Subgroups , Growth , Soluble and Polycyclic Groups , Nilpotent Groups , Isoperimetric Inequalities , Groups of Linear Growth , Linear Growth , Linear Growth Functions , The Growth of Nilpotent Groups , Polynomial Growth of Nilpotent Groups , Groups of Small Degree , The Growth of Soluble Groups , Soluble Groups of Polynomial Growth , Uniform Exponential Growth of Soluble Groups , Linear Groups , Asymptotic Cones , Groups of Polynomial Growth , Infinitely Generated Groups , Intermediate Growth: Grigorchuk's First Group , More Groups of Intermediate Growth , The General Grigorchuk Groups , Groups Acting on Regular Trees , Groups Defined by Finite Automata , Bartholdi-Erschler Groups , Growth and Amenability , Amenability and Intermediate Growth , Intermediate Growth and Residual Finiteness , Explicit Calculations , The Trefoil Group , Wreath Products , Free Products with Amalgamations and HNN-Extensions , Central Products , The Generating Function , The Growth of Free Products , Conjugacy Growth , Research Problems
    Additional Edition: Print version: ISBN 9781107657502
    Language: English
    Subjects: Mathematics
    RVK:
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  • 2
    Book
    Book
    Cambridge [u.a.] : Cambridge Univ. Press
    UID:
    gbv_682953040
    Format: IX, 199 S. , graph. Darst. , 23 cm
    Edition: 1. publ.
    ISBN: 1107657504 , 9781107657502
    Series Statement: London Mathematical Society lecture note series 395
    Note: Literaturverz. S. [187] - 194
    Additional Edition: Online-Ausg. Mann, Avinoam How groups grow Cambridge : Cambridge University Press, 2012 ISBN 9781280485503
    Additional Edition: Erscheint auch als Online-Ausgabe Mann, Avinoam How groups grow Cambridge : Cambridge University Press, 2012 ISBN 9781139095129
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Gruppentheorie ; Wachstum
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  • 3
    UID:
    almahu_9949461104702882
    Format: 1 online resource (335 p.) : , Zahlr. Abb.
    Edition: Reprint 2017
    ISBN: 9783110810387 , 9783110637199
    Series Statement: De Gruyter Proceedings in Mathematics
    Note: Frontmatter -- , Preface -- , Table of Contents -- , Photos -- , Some Results and Problems about Factorized Groups -- , Normalizers of Subnormal Subgroups -- , Isomorphisms between Homeomorphic Connected Compact-Like Abelian Groups -- , Applications of Abelian Groups and Model Theory to Algebraic Structures -- , Groups Satisfying the Minimal Condition on Non-Subnormal Subgroups -- , Metabelian Groups with All Cyclic Subgroups Subnormal of Bounded Defect -- , Locally Finite Groups Whose Sylow Subgroups Are Chernikov -- , Groups Which Are Dual to Layer-Finite -- , Soluble Products of Groups -- , Torsionfree Varieties of Metabelian Groups -- , Rings with Noetherian Groups of Units -- , On Normal Closures of Elements in Generalized FC-Groups -- , Centrality in Soluble Groups -- , Finite p-Groups in Which Subgroups Have Large Cores -- , Fixed Points Induced by the Permutation of Generators in a Free Group of Rank 2 -- , Subgroup Growth: Some Current Developments -- , Power Subgroups of Profinite Groups -- , On the 4-Levi Centre and the 4-Bell Centre of a Group -- , Varieties of Representations of Groups, Quasivarieties and Pseudovarieties of Groups -- , Groups with a Minimality Condition -- , On Groups with Chernikov Centralizer of a 2-Subgroup -- , On Torsion-Free Groups with Trivial Center -- , Groups with Pronormal Subgroups of Proper Normal Subgroups -- , Some Examples of Factorized Groups and Their Relation to Ring Theory -- , FC-Groups: Recent Progress -- , A Remark on Representations of Lattices by Subgroups -- , A Note on Commutator Laws in Groups -- , Some Finiteness Conditions in Groups -- , First-Order Group Theory -- , From Finite to Infinite Groups: a Historical Survey -- , List of Participants -- , List of Lectures -- , List of Contributors , Mode of access: Internet via World Wide Web. , In English.
    In: DGBA Mathematics - 1990 - 1999, De Gruyter, 9783110637199
    Additional Edition: ISBN 9783110143324
    Language: English
    URL: Cover
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  • 4
    Online Resource
    Online Resource
    Cambridge :Cambridge University Press,
    UID:
    almahu_9948315523902882
    Format: ix, 199 p. : , ill.
    Edition: Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.
    Series Statement: London Mathematical Society lecture note series ; 395
    Language: English
    Keywords: Electronic books.
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  • 5
    UID:
    gbv_25441690X
    Format: XVIII, 368 S , graph. Darst
    Edition: 2. ed. rev. and enl. by Marcus du Sautoy and Dan Segal
    ISBN: 0521650119 , 0521542189
    Series Statement: Cambridge studies in advanced mathematics 61
    Note: Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke
    Additional Edition: Erscheint auch als Online-Ausgabe Dixon, John D. Analytic pro-p groups Cambridge : Cambridge University Press, 1999 ISBN 9780521650113
    Additional Edition: ISBN 9780521542180
    Additional Edition: ISBN 9780511470882
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Pro-p-Gruppe
    Author information: Du Sautoy, Marcus 1965-
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