vol 4: Glossary
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Group
[Hazewinkel, Group] [Borowski, Group]
'The concept of a group is historically one of the first examples of abstract algebraic systems and served in many respects, as a model for the restructuring of other mathematical disciplines at the turn into the twentieth century, as a result of which the concept of a mathematical system (a structure) has become a fundamental concept on mathematics.
'Definition. A group is a non-empty set G with one binary operation that satisfied the following axioms (the operation being written as multiplication):
- the operation is associative, ie (ab)c = a(bc) for any a, b and c in G.
- the operation admits a unit, ie G has an element e, known as the null element such that ae = ea = a for any a in G.
- the operation admits inverse elements, ie for any a in G there exists an element x in G, said to be the inverse to a such that ax = xa = e. '
Books
| Alexandroff, P S, An Introduction to the Theory of Groups, Blackie and Son Limited 1959-1963 back |
| Borowski, Ephraim J, Collins Dictionary of Mathematics, Harper Collins 1089 'It is the immodest hope of the authors that this dictionary will not only prove valuable as a reference book for students of mathematics at all levels from secondary schools to a master's degree, but also offer much to interest a more general readership. Amazon back |
| Hazewinkel, Michiel, Encyclopaedia of Mathematics (6 volumes), Kluwer Academic and Toppan 1995 'The Encyclopaedia of mathematics aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-85.' Amazon back |
| Heine, Volker, Group Theory in Quantum Mechanics: An Introduction to its Present Usage, Dover 1993 'The object of this book is to introduce the three main uses of group theory in quantum mechanics, which are: firstly, to label energy levels and the corresponding eigenstates; secondly to discuss qualitatively the splitting of energy levels ... ; and thirdly to aid in the evaluationof matrix elements of all kinds ...' Amazon back |
| Higman, Bryan, Applied Group-Theoretic and Matrix Methods, Dover Publications back |
| Weyl, Hermann, The Theory of Groups and Quantum Mechanics, Dover 1950 Amazon back |
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