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G-theory of group rings for finite groups

dc.contributor.advisorLück, Wolfgang
dc.contributor.authorSemikina, Iuliia
dc.date.accessioned2020-04-25T13:18:28Z
dc.date.available2020-04-25T13:18:28Z
dc.date.issued13.12.2018
dc.identifier.urihttps://hdl.handle.net/20.500.11811/7669
dc.description.abstractIn this thesis we investigate Quillen's G-theory of group rings mostly focusing on the case of finite groups. We study the Hambleton-Taylor-Williams decomposition conjecture for G-theory of the integral group rings. The conjecture expresses n-th G-group of the integral group ring as a direct sum of G-groups of maximal orders in the simple components of QG with certain integers inverted. The HTW-conjecture generalizes the results of Lenstra and Webb on abelian groups. Webb and Yao found a counterexample to the HTW-decomposition in degree 1 but nevertheless they still expected the conjecture to hold for solvable groups. Using the results of Keating we show that the solvable group SL(2, F3) is a counterexample to the conjectured decomposition. Using the methods from modular representation theory we prove useful inequality for ranks of G-groups in degree 1. It is also shown that the HTW-decomposition gives a correct prediction for the torsion subgroup in degree 1 for all finite groups G. Furthermore, we prove that the ranks of G-groups in degree n agree with the prediction of the conjecture in all degrees apart from the degree n = 1.
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematik
dc.titleG-theory of group rings for finite groups
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5n-52618
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID5261
ulbbnediss.date.accepted04.10.2018
ulbbnediss.instituteMathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeStroppel, Catharina


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