03146nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072002300183082001400206100003100220245010800251264003800359300003500397336002600432337002600458338003600484347002400520490003500544505039500579520127500974650001702249650002302266650002102289650002502310650002302335650001802358650001702376650003802393650003602431650003602467710003402503773002002537776003602557830003502593856004802628978-1-84882-941-1DE-He21320180115171546.0cr nn 008mamaa100301s2009 xxk| s |||| 0|eng d a97818488294117 a10.1007/978-1-84882-941-12doi 4aQA174-183 7aPBG2bicssc 7aMAT0020102bisacsh04a512.22231 aWehrfritz, B.A.F.eauthor.10aGroup and Ring Theoretic Properties of Polycyclic Groupsh[electronic resource] /cby B.A.F. Wehrfritz. 1aLondon :bSpringer London,c2009. aVIII, 128 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aAlgebra and Applications ;v100 aSome Basic Group Theory -- The Basic Theory of Polycyclic Groups -- Some Ring Theory -- Soluble Linear Groups -- Further Group-Theoretic Properties of Polycyclic Groups -- Hypercentral Groups and Rings -- Groups Acting on Finitely Generated Commutative Rings -- Prime Ideals in Polycyclic Group Rings -- The Structure of Modules over Polycyclic Groups -- Semilinear and Skew Linear Groups. aPolycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations. The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups. 0aMathematics. 0aAssociative rings. 0aRings (Algebra). 0aCommutative algebra. 0aCommutative rings. 0aGroup theory.14aMathematics.24aGroup Theory and Generalizations.24aAssociative Rings and Algebras.24aCommutative Rings and Algebras.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781848829404 0aAlgebra and Applications ;v1040uhttp://dx.doi.org/10.1007/978-1-84882-941-1