Archiv der Mathematik

, Volume 93, Issue 3, pp 205–211 | Cite as

Symmetric cohomology of groups in low dimension



We give an explicit characterization for group extensions that correspond to elements of the symmetric cohomology HS 2(G, A). We also give conditions for the map HS n (G, A) → H n (G, A) to be injective.

Mathematics Subject Classification (2000)

Primary 20J06 Secondary 18G60 


Symmetric cohomology Group extensions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. S. Brown, Cohomology of Groups, Graduate texts in Mathematics 87, Springer-Verlag, 1982.Google Scholar
  2. 2.
    Eilenberg S., MacLane S.: Determination of the second homology and cohomology groups of a space by means of homotopy invariants. Proc. Nat. Acad. Sci. 32, 277–280 (1946)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fiedorowicz Z., Loday J.L.: Crossed simplicial groups and their associated homology. Trans. Amer. Math. Soc. 326, 57–87 (1991)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    M. D. Staic, From 3-algebras to Δ-groups and Symmetric Cohomology, J. Algebra (4) 332 (2009), 1360–1378.Google Scholar
  5. 5.
    S. Van Ault, private communication.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Institute of Mathematics of the Romanian AcademyBucharestRomania

Personalised recommendations