• About
  • Policies
  • What is open access
  • Library
  • Contact
Advanced search
      View Item 
      •   BUIR Home
      • Scholarly Publications
      • Faculty of Science
      • Department of Mathematics
      • View Item
      •   BUIR Home
      • Scholarly Publications
      • Faculty of Science
      • Department of Mathematics
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

      Generalized Burnside rings and group cohomology

      Thumbnail
      View / Download
      249.6 Kb
      Author(s)
      Hartmann, R.
      Yalçın, E.
      Date
      2007-04-15
      Source Title
      Journal of Algebra
      Print ISSN
      0021-8693
      Electronic ISSN
      1090-266X
      Publisher
      Academic Press
      Volume
      310
      Pages
      917 - 944
      Language
      English
      Type
      Article
      Item Usage Stats
      183
      views
      211
      downloads
      Abstract
      We define the cohomological Burnside ring B n (G, M) of a finite group G with coefficients in a Z G-module M as the Grothendieck ring of the isomorphism classes of pairs [X, u] where X is a G-set and u is a cohomology class in a cohomology group H X n (G, M). The cohomology groups H X * (G, M) are defined in such a way that H X * (G, M) ≅ ⊕ i H * (H i, M) when X is the disjoint union of transitive G-sets G / H i. If A is an abelian group with trivial action, then B 1 (G, A) is the same as the monomial Burnside ring over A, and when M is taken as a G-monoid, then B 0 (G, M) is equal to the crossed Burnside ring B c (G, M). We discuss the generalizations of the ghost ring and the mark homomorphism and prove the fundamental theorem for cohomological Burnside rings. We also give an interpretation of B 2 (G, M) in terms of twisted group rings when M = k × is the unit group of a commutative ring. © 2006 Elsevier Inc. All rights reserved.
      Keywords
      Cohomology of groups
      Generalized Burnside rings
      Monomial G-sets
      Permalink
      http://hdl.handle.net/11693/11588
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.jalgebra.2006.10.037
      Collections
      • Department of Mathematics 712
      Show full item record

      Browse

      All of BUIRCommunities & CollectionsTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartmentsCoursesThis CollectionTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartmentsCourses

      My Account

      Login

      Statistics

      View Usage StatisticsView Google Analytics Statistics

      Bilkent University

      If you have trouble accessing this page and need to request an alternate format, contact the User and Access Services. Phone: (312) 290 1298
      © Bilkent University - Library IT

      Contact Us | Send Feedback | Off-Campus Access | Admin | Privacy