The Rational Function Analogue of a Question of Schur and Exceptionality of Permutation Representations

, by Guralnick, Robert M.; Muller, Peter; Saxl, J.

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ISBN: 9780821832882 | 0821832883
Cover: Hardcover
Copyright: 3/1/2003

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Supplemental Materials

Introduction	p. 1
Arithmetic-Geometric Preparation	p. 6
Arithmetic and geometric monodromy groups	p. 6
Distinguished conjugacy classes of inertia generators	p. 6
Branch cycle descriptions	p. 6
The branch cycle argument	p. 7
Weak rigidity	p. 8
Topological interpretation	p. 9
Group theoretic translation of arithmetic exceptionality	p. 10
Remark about exceptional functions over finite fields	p. 10
Group Theoretic Exceptionality	p. 12
Notation and definitions	p. 12
Primitive groups	p. 13
General results on exceptionality	p. 13
Examples of exceptionality	p. 16
Nonabelian regular normal subgroups	p. 19
Product action	p. 20
Diagonal action	p. 20
Almost simple groups	p. 22
Genus 0 Condition	p. 36
Genus 0 systems in finite permutation groups	p. 36
Diagonal action	p. 39
Product action	p. 40
Almost simple groups	p. 42
Affine action	p. 46
Dickson Polynomials and Redei Functions	p. 51
Rational Functions with Euclidean Signature	p. 53
Elliptic Curves	p. 53
Non-existence results	p. 55
Existence results	p. 59
Sporadic Cases of Arithmetic Exceptionality	p. 70
G = C[subscript 2] x C[subscript 2] (Theorem 4.13(a)(iii))	p. 70
G = (C[superscript 2 subscript 11]) [times sign, right closed] GL[subscript 2](3) (Theorem 4.13(c)(i))	p. 71
G = (C[superscript 2 subscript 5]) [times sign, right closed] S[subscript 3] (Theorem 4.13(c)(ii))	p. 72
G = (C[superscript 2 subscript 5]) [times sign, right closed] ((C[subscript 4] x C[subscript 2]) [times sign, right closed] C[subscript 2]) (Theorem 4.13(c)(iii))	p. 73
G = (C[superscript 2 subscript 5]) [times sign, right closed] D[subscript 12] (Theorem 4.13(c)(iv))	p. 73
G = (C[superscript 2 subscript 3]) [times sign, right closed] D[subscript 8] (Theorem 4.13(c)(v))	p. 73
G = (C[superscript 4 subscript 2]) [times sign, right closed] (C[subscript 5] [times sign, right closed] C[subscript 2]) (Theorem 4.13(c)(vi))	p. 73
G = PSL[subscript 2](8) (Theorem 4.10(a))	p. 73
G = PSL[subscript 2](9) (Theorem 4.10(b))	p. 75
A remark about one of the sporadic cases	p. 75
Bibliography	p. 77
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The Rational Function Analogue of a Question of Schur and Exceptionality of Permutation Representations

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The Rational Function Analogue of a Question of Schur and Exceptionality of Permutation Representations

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