LEADER 03557nam 22007575 450 001 996466518603316 005 20200705015849.0 010 $a3-540-85818-0 024 7 $a10.1007/978-3-540-85818-8 035 $a(CKB)1000000000546288 035 $a(SSID)ssj0000679710 035 $a(PQKBManifestationID)11399251 035 $a(PQKBTitleCode)TC0000679710 035 $a(PQKBWorkID)10624941 035 $a(PQKB)11476698 035 $a(DE-He213)978-3-540-85818-8 035 $a(MiAaPQ)EBC3063523 035 $a(PPN)131119427 035 $a(EXLCZ)991000000000546288 100 $a20100301d2009 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLower Central and Dimension Series of Groups$b[electronic resource] /$fby Roman Mikhailov, Inder Bir Singh Passi 205 $a1st ed. 2009. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009. 215 $a1 online resource (XXII, 352 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1952 300 $a"ISSN electronic edition 1617-9692." 311 $a3-540-85817-2 320 $aIncludes bibliographical references and index. 327 $aLower Central Series -- Dimension Subgroups -- Derived Series -- Augmentation Powers -- Homotopical Aspects -- Miscellanea. 330 $aA fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series, which consists of the subgroups determined by the augmentation powers, is a challenging task. This monograph presents an exposition of different methods for investigating this relationship. In addition to group theorists, the results are also of interest to topologists and number theorists. The approach is mainly combinatorial and homological. A novel feature is an exposition of simplicial methods for the study of problems in group theory. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1952 606 $aGroup theory 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aAlgebraic topology 606 $aAssociative rings 606 $aRings (Algebra) 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 615 0$aGroup theory. 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 0$aAlgebraic topology. 615 0$aAssociative rings. 615 0$aRings (Algebra). 615 14$aGroup Theory and Generalizations. 615 24$aCategory Theory, Homological Algebra. 615 24$aAlgebraic Topology. 615 24$aAssociative Rings and Algebras. 676 $a512.6 686 $a510$2sdnb 686 $aMAT 200f$2stub 686 $aSI 850$2rvk 700 $aMikhailov$b Roman$4aut$4http://id.loc.gov/vocabulary/relators/aut$0315665 702 $aPassi$b Inder Bir Singh$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a996466518603316 996 $aLower Central and Dimension Series of Groups$92831924 997 $aUNISA LEADER 01923nam0 2200421 i 450 001 VAN00125670 005 20250116023644.263 017 70$2N$a9783319918969 100 $a20191129d2018 |0itac50 ba 101 $aeng 102 $aCH 105 $a|||| ||||| 181 $ai$b e 182 $ab 200 1 $aSemiconductor Nanotechnology$eAdvances in Information and Energy Processing and Storage$fStephen M. 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