Symmetry Rules pp 161-194 | Cite as

The Mathematics of Symmetry: Group Theory

Part of the The Frontiers Collection book series (FRONTCOLL)


This chapter forms the start of an introduction to group theory, the mathematical language of symmetry. In it are discussed the most fundamental of the fundamental concepts and ideas of group theory. Here is a list of the more important concepts discussed in each section. Sect. 8.1: element, group, order, composition, closure, associativity, identity element, inverse element, noncommuting elements, commuting elements, Abelian (commutative) group, group structure, group table, realization. Sect. 8.2: mapping, object, image, many-to-one mapping, one-to-one mapping, into mapping, onto mapping, inverse mapping. Sect. 8.3: isomorphism. Sect. 8.4: homomorphism, kernel. Sect. 8.5: subgroup, proper subgroup.


Group Theory Identity Element Proper Subgroup Identity Transformation Abstract Group 
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© Springer-Verlag Berlin Heidelberg 2008

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