Groups pp 289-325 | Cite as

Extensions and Cohomology

  • Antonio Machì
Part of the UNITEXT book series (UNITEXT)


Among the subjects we shall touch upon in this chapter there is that of extensions. We have already mentioned this problem in Chapter 2 when talking about Höolder’s program for the classification of finite groups. As we shall see, the solution proposed by Schreier in the years 1920’s allows a classification of the groups that are extensions of an abelian group A by a group π by means of equivalence classes of functions π×π → A. Unfortunately, one does not obtain a system of invariants for the isomorphism classes of the groups obtained in this way, because nonequivalent functions can yield isomorphic groups. No characterization of the isomorphism classes is known.


Abelian Group Finite Group Isomorphism Class Cohomology Group Choice Function 
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© Springer-Verlag Italia 2012

Authors and Affiliations

  • Antonio Machì
    • 1
  1. 1.Department of MathematicsUniversity La SapienzaRomeItaly

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