【内容提要】
本书为D·E·卢瑟福的经典著作，讲述了对称群的初步观点，主要有导数的计算、杨氏公式、基偶数导数，表的计算、正交和自然表示法，不变量二次方程、矩阵、群的特性，代换方程等内容. 本书语言简洁易懂，实用与本科及研究生参考阅读.
【目 录】
Chapter Ⅰ THE CALCUIUS OF PERMUTATIONS
1 Permutations
2 The Symmetric Group
3 Cycles and Transpositions
4 Odd and Even Permutations
5 Classes of Permutations
6 Substitutional Expressions
7 The Positive and .Negative Symmetric Groups on r Letters
Chapter Ⅱ THE CALCULUS OF TABIEAUX
1 Shapes and Tableaux
2 The Substitutional Expressions P and N
3 The Product
4 The Expressions
5 von Neumann's Theorem
6 Young's Formula
7 Tableaux of Different Shapes
Chapter Ⅲ THE SEMI-NORMAL REPRESENTATION
1 Standard Tableaux
2 The Evaluation of
3 The Semi-normal Units
4 Certain Fundamental Formulae
5 The Irreducible Semi -normal Representations of
6 Expressions which do not Involve the Last Letter
7 The Semi-normal Matrix for
8 The Matrices
9 The Matrices
Chapter Ⅳ THE ORTHOGONAL AND NATURAL REPRESENTATIONS
1 Equivalent Representations
2 The Invariant Quadratic
3 The Tableau Function
4 The Orthogonal Representation
5 The Matrix
6 The Natural Representation
7 Expressions for the Units
8 Equivalence of the Natural and Semi-normal Representations
Chapter V GROUP CHARACTERS
1 The Expressions
2 The Expressions
3 The Relations between the Expressions and
4 The Group Characters of
5 The Evaluation of the Group Characters
6 Reduction Formulae
7 Littlewood's Theorem
Chapter VI SUBSTITUTIONAL EQUATIONS
1 Minimum Functions
2 The Master Idempotent
3 The Substitutional Properties of Functions
4 The Number of Independent Solutions of
5 The Solution of the Equation
6 Functions which are Invariant under a Group of Substitutional Expres-Sions
7 Some Special Cases
8 The Equation
Appendix TABLES FOR THE CASE
Bibliography
Index