Chain maps between Gruenberg resolutions

Date
2018-07
Advisor
Yalçın, Ergün
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Bilkent University
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Language
English
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Thesis
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Abstract

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.

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Keywords
Projective Resolution, Cohomology, Gruenberg Resolution, Chain Map
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Published Version (Please cite this version)