TY  - BOOK
AU  - Guralnick,Robert M.
AU  - Müller,Peter
AU  - Saxl,Jan
TI  - Rational Function Analogue of a Question of Schur and Exceptionality of Permutation Representations
T2  - Memoirs of the American Mathematical Society
SN  - 9781470403713
AV  - QA247 -- .G87 2003eb 
U1  - 512/.3 
PY  - 2003///
CY  - Providence
PB  - American Mathematical Society
KW  - Algebraic fields
KW  - Arithmetic functions
KW  - Permutation groups
KW  - Polynomials
KW  - Electronic books
N1  - Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. Arithmetic-Geometric Preparation -- 2.1. Arithmetic and geometric monodromy groups -- 2.2. Distinguished conjugacy classes of inertia generators -- 2.3. Branch cycle descriptions -- 2.4. The branch cycle argument -- 2.5. Weak rigidity -- 2.6. Topological interpretation -- 2.7. Group theoretic translation of arithmetic exceptionality -- 2.8. Remark about exceptional functions over finite fields -- Chapter 3. Group Theoretic Exceptionality -- 3.1. Notation and definitions -- 3.2. Primitive groups -- 3.3. General results on exceptionality -- 3.4. Examples of exceptionality -- 3.5. Nonabelian regular normal subgroups -- 3.6. Product action -- 3.7. Diagonal action -- 3.8. Almost simple groups -- Chapter 4. Genus 0 Condition -- 4.1. Genus 0 systems in finite permutation groups -- 4.2. Diagonal action -- 4.3. Product action -- 4.4. Almost simple groups -- 4.5. Affine action -- Chapter 5. Dickson Polynomials and Rédei Functions -- Chapter 6. Rational Functions with Euclidean Signature -- 6.1. Elliptic Curves -- 6.2. Non-existence results -- 6.3. Existence results -- Chapter 7. Sporadic Cases of Arithmetic Exceptionality -- 7.1. G = C[sub(2)] x C[sub(2)] (Theorem 4.13(a)(iii)) -- 7.2. G = (C[sup(2)][sub(11)]) x GL[sub(2)(3) (Theorem 4.13(c)(1)) -- 7.3. G = (C[sup(2)][sub(11)]) x S[sub(3)] (Theorem 4.13(c)(ii)) -- 7.4. G = (C[sup(2)][sub(5)]) x ((C[sub(4)] x C[sub(2)]) x C[sub(2)]) (Theorem 4.13(c)(iii)) -- 7.5. G = (C[sup(2)][sub(5)]) x D[sub(12)] (Theorem 4.13(c)(iv)) -- 7.6. G = (C[sup(2)][sub(3)]) x D[sub(8)] (Theorem 4.13(c)(v)) -- 7.7. G = (C[sup(4)][sub(2)]) x (C[sup(5)] x C[sub(2)]) (Theorem 4.13(c)(vi)) -- 7.8. G = PSL[sub(2)](8) (Theorem 4.10(a)) -- 7.9. G = PSL[sub(2)](9) (Theorem 4.10(b)) -- 7.10. A remark about one of the sporadic cases -- Bibliography
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