Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I : Generic Covers and Covers with Many Branch Points.

Intro -- Contents -- Chapter 1. Introduction and statement of main results -- 1.1. Five or more branch points -- 1.2. An n-cycle -- 1.3. Asymptotic behavior of the genus for actions on k-sets -- 1.4. Galois groups of trinomials -- Chapter 2. Notation and basic lemmas -- Chapter 3. Examples -- Chapter 4. Proving the main results on five or more branch points - Theorems 1.1.1 and 1.1.2 -- Chapter 5. Actions on 2-sets - the proof of Theorem 4.0.30 -- Chapter 6. Actions on 3-sets - the proof of Theorem 4.0.31 -- Chapter 7. Nine or more branch points - the proof of Theorem 4.0.34 -- Chapter 8. Actions on cosets of some 2-homogeneous and 3-homogeneous groups -- Chapter 9. Actions on 3-sets compared to actions on larger sets -- Chapter 10. A transposition and an n-cycle -- Chapter 11. Asymptotic behavior of g[sub(k)] (E) -- Chapter 12. An n-cycle - the proof of Theorem 1.2.1 -- Chapter 13. Galois groups of trinomials - the proofs of Propositions 1.4.1 and 1.4.2 and Theorem 1.4.3 -- Appendix A. Finding small genus examples by computer search -- A.1. Description -- A.2. n = 5 and n = 6 -- A.3. 5 ≤ r ≤ 8, 7 ≤ n ≤ 20 -- A.4. r &lt -- 5 -- Bibliography.

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