# Note 6.

The term *group* comes from the mathematical theory of *Groups*. In our case a * point group* means a certain set of point symmetry operations. Between the individual elements of such a set (thus between the relevant point symmetry operations belonging to that set) one can imagine an operation to be possible, namely the execution of one such symmetry operation __folowed__ by a second one executed on the result of the first one. For example we subject a certain object first to a rotation involving a certain angle, resulting in the object to coincide with itself, and now we subject this result to a second symmetry operation, say a rotation or a reflection, resulting in the object again coinciding with itself. This means that the combined operation is itself a symmetry operation, that should be identical to one of the symmetry operations of the above mentioned set. If __any__ combination of symmetry operations of the set results in an operation that is already represented in that set, then such a set is called a group. Such a group is accordingly a more or less small mathematical system **:** It consists of elements which can be combined by means of a certain operator, in our case this operator is **:** the execution of two or more symmetry operations after each other. All such consecutively executed symmetry operations result in a symmetry operation already listed in the set. We say that the set is *closed* under the operation of combining two or more symmetry operations.

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