LEADER 04569nam 2200721Ia 450 001 9910973322303321 005 20200520144314.0 010 $a1-139-24871-5 010 $a1-107-23239-2 010 $a1-139-09512-9 010 $a1-280-48550-7 010 $a1-139-22330-5 010 $a9786613580481 010 $a1-139-21850-6 010 $a1-139-22502-2 010 $a1-139-21541-8 010 $a1-139-22159-0 035 $a(CKB)2550000000082953 035 $a(EBL)833519 035 $a(OCoLC)775870074 035 $a(SSID)ssj0000636641 035 $a(PQKBManifestationID)11403929 035 $a(PQKBTitleCode)TC0000636641 035 $a(PQKBWorkID)10676753 035 $a(PQKB)10832815 035 $a(UkCbUP)CR9781139095129 035 $a(MiAaPQ)EBC833519 035 $a(Au-PeEL)EBL833519 035 $a(CaPaEBR)ebr10533253 035 $a(CaONFJC)MIL358048 035 $a(PPN)26128665X 035 $a(EXLCZ)992550000000082953 100 $a20110815d2012 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHow groups grow /$fAvinoam Mann 205 $a1st ed. 210 $aCambridge $cCambridge University Press$d2012 215 $a1 online resource (ix, 199 pages) $cdigital, PDF file(s) 225 1 $aLondon Mathematical Society lecture note series ;$v395 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 08$a1-107-65750-4 320 $aIncludes bibliographical references (p. [187]-194) and index. 327 $g1$tIntroduction$g1 --$g2$tSome Group Theory$g15 --$g2.1$tFinite Index Subgroups$g15 --$g2.2$tGrowth$g18 --$g2.3$tSoluble and Polycyclic Groups$g25 --$g2.4$tNilpotent Groups$g27 --$g2.5$tIsoperimetric Inequalities$g32 --$g3$tGroups of Linear Growth$g36 --$g3.1$tLinear Growth$g36 --$g3.2$tLinear Growth Functions$g41 --$g4$tThe Growth of Nilpotent Groups$g44 --$g4.1$tPolynomial Growth of Nilpotent Groups$g44 --$g4.2$tGroups of Small Degree$g50 --$g5$tThe Growth of Soluble Groups$g56 --$g5.1$tSoluble Groups of Polynomial Growth$g56 --$g5.2$tUniform Exponential Growth of Soluble Groups$g60 --$g6$tLinear Groups$g63 --$g7$tAsymptotic Cones$g67 --$g8$tGroups of Polynomial Growth$g77 --$g9$tInfinitely Generated Groups$g81 --$g10$tIntermediate Growth: Grigorchuk's First Group$g90 --$g11$tMore Groups of Intermediate Growth$g108 --$g11.1$tThe General Grigorchuk Groups$g108 --$g11.2$tGroups Acting on Regular Trees$g113 --$g11.3$tGroups Defined by Finite Automata$g115 --$g11.4$tBartholdi-Erschler Groups$g119 --$g12$tGrowth and Amenability$g121 --$g12.1$tAmenability and Intermediate Growth$g121 --$g12.2tMore Isoperimetric Inequalities$g127 --$g13$tIntermediate Growth and Residual Finiteness$g131 --$g14$tExplicit Calculations$g136 --$g14.1$tThe Trefoil Group$g136 --$g14.2$tWreath Products$g139 --$g14.3$tFree Products with Amalgamations and HNN-Extensions$g141 --$g14.4$tCentral Products$g146 --$g15$tThe Generating Function$g148 --$g16$tThe Growth of Free Products$g158 --$g17$tConjugacy Growth$g176 --$g18$tResearch Problems$g185. 330 $aGrowth of groups is an innovative new branch of group theory. This is the first book to introduce the subject from scratch. It begins with basic definitions and culminates in the seminal results of Gromov and Grigorchuk and more. The proof of Gromov's theorem on groups of polynomial growth is given in full, with the theory of asymptotic cones developed on the way. Grigorchuk's first and general groups are described, as well as the proof that they have intermediate growth, with explicit bounds, and their relationship to automorphisms of regular trees and finite automata. Also discussed are generating functions, groups of polynomial growth of low degrees, infinitely generated groups of local polynomial growth, the relation of intermediate growth to amenability and residual finiteness, and conjugacy class growth. This book is valuable reading for researchers, from graduate students onward, working in contemporary group theory. 410 0$aLondon Mathematical Society lecture note series ;$v395. 606 $aGroup theory 606 $aAlgorithms 615 0$aGroup theory. 615 0$aAlgorithms. 676 $a512.2 686 $aMAT 200f$2stub 700 $aMann$b Avinoam$f1937-$0477391 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910973322303321 996 $aHow groups grow$9239908 997 $aUNINA