TY  - BOOK
AU  - Guralnick,Robert M.
AU  - Shareshian,John
TI  - Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I: Generic Covers and Covers with Many Branch Points
T2  - Memoirs of the American Mathematical Society
SN  - 9781470404901
AV  - QA175 -- .G87 2007eb 
U1  - 512.21 
PY  - 2007///
CY  - Providence
PB  - American Mathematical Society
KW  - Permutation groups
KW  - Curves
KW  - Monodromy groups
KW  - Riemann surfaces
KW  - Symmetry groups
KW  - Electronic books
N1  - 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114137
ER  -