G-theory of group rings for finite groups
G-theory of group rings for finite groups
dc.contributor.advisor | Lück, Wolfgang | |
dc.contributor.author | Semikina, Iuliia | |
dc.date.accessioned | 2020-04-25T13:18:28Z | |
dc.date.available | 2020-04-25T13:18:28Z | |
dc.date.issued | 13.12.2018 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/7669 | |
dc.description.abstract | In 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.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject.ddc | 510 Mathematik | |
dc.title | G-theory of group rings for finite groups | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5n-52618 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 5261 | |
ulbbnediss.date.accepted | 04.10.2018 | |
ulbbnediss.institute | Mathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Stroppel, Catharina |
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