Introduction to Abstract Algebra ( Math 113 )
نویسندگان
چکیده
3 Groups 12 3.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Subgroups, Cosets and Lagrange’s Theorem . . . . . . . . . . . . . . . . . . 14 3.3 Finitely Generated Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4 Permutation Groups and Group Actions . . . . . . . . . . . . . . . . . . . . 19 3.5 The Oribit-Stabiliser Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.6 Finite Symmetric Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.7 Symmetry of Sets with Extra Structure . . . . . . . . . . . . . . . . . . . . . 28 3.8 Normal Subgroups and Isomorphism Theorems . . . . . . . . . . . . . . . . . 30 3.9 Direct Products and Direct Sums . . . . . . . . . . . . . . . . . . . . . . . . 36 3.10 Finitely Generated Abelian Groups . . . . . . . . . . . . . . . . . . . . . . . 37 3.11 Finite Abelian Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
منابع مشابه
Some notes on sets , logic , and mathematical language
These are ‘‘generic’’ notes, for use in Math 110, 113, 104 or 185. (This printing is adapted for use in Math 110 with Friedberg, Insel and Spence’s Linear Algebra. Part 1 below has a large overlap with Appendices A and B of that text, but I have left it in for completeness, and because it gives further examples of the concepts in question.) These pages do not develop in detail the definitions a...
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1. A. Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Bull. Amer. Math. Soc. 67 (1961), 579-583. 2. , Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485-535. 3. Harish-Chandra, On the characters of a semisimple Lie group, Bull. Amer. Math. Soc. 61 (1955), 389-396. 4. , Differential operators on a semisimple Lie algebra, Amer. J. Math. 79 (1957), 87-12...
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