Mac Lane Method for Determination of Extensions of Finite Groups. II. An Example for the Dihedral Group D2
T. Lulek
Institute of Physics, A. Mickiewicz University, Matejki 48/49, 60-769 PoznaƄ, Poland

and R. Chatterjee
Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada
Received: May 28, 1992
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The Mac Lane method of classification and construction of all extensions of a group Q by an Abelian group T is demonstrated on the case Q = D2, T = C2. Constructions involving free groups and operator homomorphisms are performed in detail, and the complete list of resulting extensions is given. It is shown that there are 8 classes of gauge equivalency, and they fall into 4 classes of isomorphism. The role of gauge transformations is pointed out. Physical contexts of various constructions are reviewed. A comparison with the direct cohomology definitions is performed.
DOI: 10.12693/APhysPolA.82.395
PACS numbers: 02.20.+b, 02.40.+m, 03.20.+i, 11.30.Er