Stallings-Stammbach sequence
From Groupprops
Definition
The Stallings-Stammbach sequence is a slight generalization of the Stallings exact sequence. Suppose we have a short exact sequence of groups:
Suppose that is a -module, i.e., an abelian group equipped with a homomorphism of groups:
The Stallings-Stammbach sequence is the following short exact sequence of groups:
In the case that with trivial action of on it, the Stallings-Stammback sequence becomes the Stallings exact sequence.
References
- On the homology theory of central group extensions: I—The commutator map and stem extensions by Beno Eckmann, Peter J. Hilton and Urs Stammbach, Commentarii Mathematici Helvetici, Volume 47,Number 1, Page 102 - 122(Year 1972): ^{Official copy (gated)}^{More info}, (1.2) (first page of the paper)