## Group Theory: An Intuitive ApproachA thorough introduction to group theory, this (highly problem-oriented) book goes deeply into the subject to provide a fuller understanding than available anywhere else. The book aims at, not only teaching the material, but also helping to develop the skills needed by a researcher and teacher, possession of which will be highly advantageous in these very competitive times, particularly for those at the early, insecure, stages of their careers. And it is organized and written to serve as a reference to provide a quick introduction giving the essence and vocabulary useful for those who need only some slight knowledge, those just learning, as well as researchers, and especially for the latter it provides a grasp, and often material and perspective, not otherwise available. |

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### Contents

The Physical Principles of Group Theory | 1 |

n Examples of Groups | 29 |

Groups as Mathematical Objects | 67 |

a1 Group Table for Cn | 68 |

e2 Group Table for the Quaternion Group | 75 |

i1 Group Table for a Nongroup | 81 |

Groups Combinations Subsets | 106 |

Representations | 146 |

VfflThe Symmetric Group and its Representations | 214 |

STATES OF THE ORTHOGONAL CATEGORY | 233 |

Properties and Applications of Symmetric Groups | 248 |

The Rotation Groups and their Relatives | 269 |

Representations of Groups SO3 and SU2 | 304 |

Xn Applications of Representations of SO3 and O3 | 339 |

Xffl Lie Algebras | 367 |

XTV Representations of Lie Algebras | 402 |

The Group as a Representation of Itself | 170 |

Vn Properties of Representations | 180 |

A SU3 and States of Some of its Representations | 427 |

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### Common terms and phrases

Abelian group angles angular momentum antisymmetric atom automorphism axes axis basis vectors Baumslag and Chandler Check coefficients commutation relations complete conjugate consider coordinates cosets cyclic group defined determined diagonal dihedral groups dimension direct product eigenvalues equation equivalence classes examples factor group finite group form a group frames functions geometrical give given group axioms group elements group operators group sec group table group theory Hamermesh 1962 Hamiltonian homomorphic identity infinite integer invariant subgroup inverse irreducible representations isomorphic isospin labeled Ledermann 1953 Lie algebra Lie groups linear mathematical matrix elements Mirman monomial multinomials multiplication nonzero normal subgroup objects orthogonal orthonormal parameters permutations physical Problem properties Prove quantum mechanics realization reducible regular representation representation matrices roots rotation group scalar semisimple sentations Show similarity transformation simple space square statefunctions subalgebra subset symbols symmetric groups symmetry tableaux tation theorem tions transpositions unitary