This text provides an easy to follow introduction to the theory of groups and of group characters. The author presents group theory through the Sylow Theorems and uses many worked-out examples, including the full subgroup structure of A5. Representations and characters are worked out with numerous character tables plus real and induced characters that lead to the table for S5. The book includes sections that provide the mathematical basis for some of the applications of group theory in spectroscopy and molecular structure. It is also full of exercises that five the reader a sense of the applications to larger projects.…mehr
This text provides an easy to follow introduction to the theory of groups and of group characters. The author presents group theory through the Sylow Theorems and uses many worked-out examples, including the full subgroup structure of A5. Representations and characters are worked out with numerous character tables plus real and induced characters that lead to the table for S5. The book includes sections that provide the mathematical basis for some of the applications of group theory in spectroscopy and molecular structure. It is also full of exercises that five the reader a sense of the applications to larger projects.
Preface 1 Introductory Examples 2 Groups and Subgroups 3 Point Groups and Cosets 4 Homomorphisms and Normal Subgroups 5 Isomorphisms and Automorphisms 6 Factor Groups 7 Sylow Subgroups 8 Permutation Groups 9 Matrix Groups 10 Group Representations 11 Regular Representations 12 Irreducible Representations 13 Representations of Abelian Groups 14 Group Characters 15 Orthogonality Relations and Character Tables 16 Reducible Characters 17 The Burnside Counting Theorem 18 Real Characters 19 Induced Characters 20 The Character Table for S5 21 Space Groups and Semidirect Products 22 Proofs of the Sylow Theorems Bibliography Index of Symbols Index
Preface 1 Introductory Examples 2 Groups and Subgroups 3 Point Groups and Cosets 4 Homomorphisms and Normal Subgroups 5 Isomorphisms and Automorphisms 6 Factor Groups 7 Sylow Subgroups 8 Permutation Groups 9 Matrix Groups 10 Group Representations 11 Regular Representations 12 Irreducible Representations 13 Representations of Abelian Groups 14 Group Characters 15 Orthogonality Relations and Character Tables 16 Reducible Characters 17 The Burnside Counting Theorem 18 Real Characters 19 Induced Characters 20 The Character Table for S5 21 Space Groups and Semidirect Products 22 Proofs of the Sylow Theorems Bibliography Index of Symbols Index
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