The third cohomology group classifies crossed module extensions

Sebastian Thomas

We give an elementary proof of the well-known fact that the third cohomology group H^3(G, M) of a group G with coefficients in an abelian G-module M is in bijection to the set Ext^2(G, M) of equivalence classes of crossed module extensions of G with M.

fulltext, arXiv:0911.2861

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