Low-Dimensional Cohomology and Group Extensions
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
[Warning: Some people call this an extension of N by G.] A second extension 1 → N → E′ → G → 1 of G by N is said to be equivalent to (*) if there is a map E → E′ making the diagram commute. Note that such a map is necessarily an isomorphism.
$$ 1 \to N \to E \to G \to 1. $$
KeywordsExact Sequence Normal Subgroup Central Extension Cyclic Subgroup Finite Index
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© Springer-Verlag New York Inc. 1982