Mac Lane Method for Determination of Extensions of Finite Groups. I. A Review in the Context of Structure of Condensed Matter

The problem of classification of all extensions of a finite group Q by an Abelian group T has been reviewed using cohomology of groups and fibre bundle picture. The relevance of this problem in condensed matter physics has been pointed out in the context of crystallography and gauge fields. The Mac Lane method of an effective construction of the corresponding second cohomology group as the quotient group of all operator homomorphisms vs. crossed homomorphisms from some free groups to T has been described in detail.