Group theory definition

As described in Section I, the CSM of a set of points with respect to a given symmetry group G is evaluated by first finding the set of points which is G-sym-metric and which is closest to the given set in terms of the average distance squared. We must thus prove that the folding method indeed finds the closest symmetric set of points. The group-theory definitions which are used in this section, are briefly reviewed in Appendix B. 

A group is a collection of elements that are interrelated according to certain rules. We need not specify what the elements are or attribute any physical significance to them in order to discuss the group which they constitute. In this book, of course, we shall be concerned with the groups formed by the sets of symmetry operations that may be carried out on molecules or crystals, but the basic definitions and theorems of group theory are far more general. 

In this section, we provide a succinct survey of the definitions and results of group theory required for a group-theoretical formulation of quantum and classical mechanics, which are the objects of the following sections. 

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