Fidan, Müge2018-08-032018-08-032018-072018-072018-08-02http://hdl.handle.net/11693/47726Cataloged from PDF version of article.Thesis (M.S.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2018.Includes bibliographical references (leaves 56-57).Let G be a finite group. For a given presentation of G = hF|Ri, Gruenberg gives a construction of a projective resolution for Z as a ZG-module. This resolution, which is called Gruenberg resolution, only depends on the ideals IF := ker{ZF → Z} and J := ker{ZF → ZG} (see [1]). We write standard resolution as a Gruenberg resolution by following the construction of Gruenberg [2]. We get an explicit chain map formula between Gruenberg resolution for standard presentation and the Gruenberg resolution for the usual presentation of a cyclic group. Then we write an explicit chain map formula between any two Gruenberg resolutions. We also give some calculations with Gruenberg resolution.vii, 57 leaves ;30 cm.Englishinfo:eu-repo/semantics/openAccessProjective ResolutionCohomologyGruenberg ResolutionChain MapThesisB158753