03557nam 22007575 450 99646651860331620200705015849.03-540-85818-010.1007/978-3-540-85818-8(CKB)1000000000546288(SSID)ssj0000679710(PQKBManifestationID)11399251(PQKBTitleCode)TC0000679710(PQKBWorkID)10624941(PQKB)11476698(DE-He213)978-3-540-85818-8(MiAaPQ)EBC3063523(PPN)131119427(EXLCZ)99100000000054628820100301d2009 u| 0engurnn|008mamaatxtccrLower Central and Dimension Series of Groups[electronic resource] /by Roman Mikhailov, Inder Bir Singh Passi1st ed. 2009.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2009.1 online resource (XXII, 352 p.) Lecture Notes in Mathematics,0075-8434 ;1952"ISSN electronic edition 1617-9692."3-540-85817-2 Includes bibliographical references and index.Lower Central Series -- Dimension Subgroups -- Derived Series -- Augmentation Powers -- Homotopical Aspects -- Miscellanea.A 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.Lecture Notes in Mathematics,0075-8434 ;1952Group theoryCategory theory (Mathematics)Homological algebraAlgebraic topologyAssociative ringsRings (Algebra)Group Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035Algebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Group theory.Category theory (Mathematics).Homological algebra.Algebraic topology.Associative rings.Rings (Algebra).Group Theory and Generalizations.Category Theory, Homological Algebra.Algebraic Topology.Associative Rings and Algebras.512.6510sdnbMAT 200fstubSI 850rvkMikhailov Romanauthttp://id.loc.gov/vocabulary/relators/aut315665Passi Inder Bir Singhauthttp://id.loc.gov/vocabulary/relators/autBOOK996466518603316Lower Central and Dimension Series of Groups2831924UNISA