English

The third cohomology group classifies crossed module extensions

K-Theory and Homology 2010-09-30 v2 Algebraic Topology Group Theory

Abstract

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.

Keywords

Cite

@article{arxiv.0911.2861,
  title  = {The third cohomology group classifies crossed module extensions},
  author = {Sebastian Thomas},
  journal= {arXiv preprint arXiv:0911.2861},
  year   = {2010}
}

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R2 v1 2026-06-21T14:11:47.619Z