"Group Theory 001.ps.gz" - читать интересную книгу автораGROUP THEORY J.S. MILNE August 21, 1996; v2.01 Abstract. Thes are the notes for the first part of Math 594, University of Michigan, Winter 1994, exactly as they were handed out during the course except for some minor corrections. Please send comments and corrections to me at [email protected] using "Math594" as the subject. Contents 1. Basic Definitions 1 1.1. Definitions 1 1.2. Subgroups 3 1.3. Groups of order ! 16 4 1.4. Multiplication tables 5 1.5. Homomorphisms 5 1.6. Cosets 6 1.7. Normal subgroups 7 1.8. Quotients 8 2. Free Groups and Presentations 10 2.1. Free semigroups 10 2.2. Free groups 10 2.3. Generators and relations 13 2.4. Finitely presented groups 14 The word problem The Burnside problem Todd-Coxeter algorithm Maple 3.1. Theorems concerning homomorphisms 16 Factorization of homomorphisms The isomorphism theorem The correspondence theorem Copyright 1996 J.S. Milne. You may make one copy of these notes for your own personal use. i ii J.S. MILNE 3.2. Products 17 3.3. Automorphisms of groups 18 3.4. Semidirect products 21 3.5. Extensions of groups 23 3.6. The H"older program. 24 4. Groups Acting on Sets 25 4.1. General definitions and results 25 Orbits Stabilizers Transitive actions The class equation p-groups Action on the left cosets 4.2. Permutation groups 31 4.3. The Todd-Coxeter algorithm. 35 4.4. Primitive actions. 37 |
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