Low-Dimensional Cohomology and Group Extensions

  • Kenneth S. Brown
Part of the Graduate Texts in Mathematics book series (GTM, volume 87)


An extension of a group G by a group N is a short exact sequence of groups

$$ 1 \to N \to E \to G \to 1. $$
[Warning: Some people call this an extension of N by G.] A second extension 1 → NE′ → G → 1 of G by N is said to be equivalent to (*) if there is a map EE′ making the diagram
commute. Note that such a map is necessarily an isomorphism.


Exact Sequence Normal Subgroup Central Extension Cyclic Subgroup Finite Index 


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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Kenneth S. Brown
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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