Abstract
Abstract This chapter introduces group theory and the rules governing mathematical groups, of which point groups and space groups are examples. Group multiplication tables and their uses are described with examples, and subgroups and cosets are considered briefly. Similarity transformations are used to show the equivalence, or otherwise, of symmetry operations. Character tables are introduced and explained, and the procedures for creating representations are described. Transformation properties are discussed, and irreducible representations and their notations are examined, leading to a description of the theorems on orthogonality. The construction of character tables is explained, together with the applications of direct products.
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