04569nam 2200721Ia 450 991097332230332120200520144314.01-139-24871-51-107-23239-21-139-09512-91-280-48550-71-139-22330-597866135804811-139-21850-61-139-22502-21-139-21541-81-139-22159-0(CKB)2550000000082953(EBL)833519(OCoLC)775870074(SSID)ssj0000636641(PQKBManifestationID)11403929(PQKBTitleCode)TC0000636641(PQKBWorkID)10676753(PQKB)10832815(UkCbUP)CR9781139095129(MiAaPQ)EBC833519(Au-PeEL)EBL833519(CaPaEBR)ebr10533253(CaONFJC)MIL358048(PPN)26128665X(EXLCZ)99255000000008295320110815d2012 uy 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierHow groups grow /Avinoam Mann1st ed.Cambridge Cambridge University Press20121 online resource (ix, 199 pages) digital, PDF file(s)London Mathematical Society lecture note series ;395Title from publisher's bibliographic system (viewed on 05 Oct 2015).1-107-65750-4 Includes bibliographical references (p. [187]-194) and index.1Introduction1 --2Some Group Theory15 --2.1Finite Index Subgroups15 --2.2Growth18 --2.3Soluble and Polycyclic Groups25 --2.4Nilpotent Groups27 --2.5Isoperimetric Inequalities32 --3Groups of Linear Growth36 --3.1Linear Growth36 --3.2Linear Growth Functions41 --4The Growth of Nilpotent Groups44 --4.1Polynomial Growth of Nilpotent Groups44 --4.2Groups of Small Degree50 --5The Growth of Soluble Groups56 --5.1Soluble Groups of Polynomial Growth56 --5.2Uniform Exponential Growth of Soluble Groups60 --6Linear Groups63 --7Asymptotic Cones67 --8Groups of Polynomial Growth77 --9Infinitely Generated Groups81 --10Intermediate Growth: Grigorchuk's First Group90 --11More Groups of Intermediate Growth108 --11.1The General Grigorchuk Groups108 --11.2Groups Acting on Regular Trees113 --11.3Groups Defined by Finite Automata115 --11.4Bartholdi-Erschler Groups119 --12Growth and Amenability121 --12.1Amenability and Intermediate Growth121 --12.2tMore Isoperimetric Inequalities127 --13Intermediate Growth and Residual Finiteness131 --14Explicit Calculations136 --14.1The Trefoil Group136 --14.2Wreath Products139 --14.3Free Products with Amalgamations and HNN-Extensions141 --14.4Central Products146 --15The Generating Function148 --16The Growth of Free Products158 --17Conjugacy Growth176 --18Research Problems185.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.London Mathematical Society lecture note series ;395.Group theoryAlgorithmsGroup theory.Algorithms.512.2MAT 200fstubMann Avinoam1937-477391MiAaPQMiAaPQMiAaPQBOOK9910973322303321How groups grow239908UNINA