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      Chain maps between Gruenberg resolutions

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      Author
      Fidan, Müge
      Advisor
      Yalçın, Ergün
      Date
      2018-08
      Publisher
      Bilkent University
      Language
      English
      Type
      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.
      Keywords
      Projective Resolution
      Cohomology
      Gruenberg Resolution
      Chain Map
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      http://hdl.handle.net/11693/47726
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      • Dept. of Mathematics - Master's degree 124
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