Cohomology of Groups

  • P. J. Hilton
  • U. Stammbach
Part of the Graduate Texts in Mathematics book series (GTM, volume 4)


In this chapter we shall apply the theory of derived functors to the important special case where the ground ring Λ is the group ring ℤ G of an abstract group G over the integers. This will lead us to a definition of cohomology groups H n (G, A) and homology groups H n (G, B), n ≧ 0, where A is a left and B a right G-module (we speak of “G-modules” instead of “ℤG-modules”). In developing the theory we shall attempt to deduce as much as possible from general properties of derived functors. Thus, for example, we shall give a proof of the fact that H 2 (G, A) classifies extensions which is not based on a particular (i.e. standard) resolution.


Exact Sequence Homology Group Short Exact Sequence Group Homomorphism Free Abelian Group 


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Copyright information

© Springer Science+Business Media New York 1971

Authors and Affiliations

  • P. J. Hilton
    • 1
    • 2
  • U. Stammbach
    • 3
  1. 1.Battelle Memorial InstituteSeattleUSA
  2. 2.Department of Mathematics and StatisticsCase Western Reserve UniversityClevelandUSA
  3. 3.Mathematisches InstitutEidgenössische Technische HochschuleZurichSwitzerland

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