03094nam 2200661 450 991046080540332120210501004650.03-11-041150-43-11-041275-610.1515/9783110411508(CKB)3710000000519824(SSID)ssj0001589546(PQKBManifestationID)16275275(PQKBTitleCode)TC0001589546(PQKBWorkID)14872553(PQKB)11243217(MiAaPQ)EBC4338472(DE-B1597)445700(OCoLC)1013942977(OCoLC)940677778(DE-B1597)9783110411508(Au-PeEL)EBL4338472(CaPaEBR)ebr11146715(CaONFJC)MIL888855(OCoLC)935640945(EXLCZ)99371000000051982420160212h20162016 uy 0engurcnu||||||||txtccrGroup ring groupsVolume 2Structure theorems of unit groups /Eric Jespers, Ángel del Río MateosBerlin, Germany ;Boston, [Massachusetts] :De Gruyter,2016.©20161 online resource (228 pages) illustrationsDe Gruyter GraduateBibliographic Level Mode of Issuance: Monograph3-11-041149-0 Includes bibliographical references and indexes.Front matter --Preface --Contents --14. Free Groups --15. Hyperbolic geometry --16. Poincaré's Theorem --17. Fundamental polyhedra --18. Unit groups of orders in quaternion algebras --19. Virtually free-by-free groups --References --Index of Notation --IndexThis two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semi-simple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.De Gruyter graduate.Group ringsRings (Algebra)Electronic books.Group rings.Rings (Algebra)512.4Jespers Eric61542del Río Mateos ÁngelMiAaPQMiAaPQMiAaPQBOOK9910460805403321Group ring groups2492680UNINA