03359nam 2200625 450 991048022290332120180731044909.01-4704-0371-4(CKB)3360000000464957(EBL)3114572(SSID)ssj0000973843(PQKBManifestationID)11553854(PQKBTitleCode)TC0000973843(PQKBWorkID)10960028(PQKB)11412592(MiAaPQ)EBC3114572(PPN)195416597(EXLCZ)99336000000046495720021105d2003 uy| 0engur|n|---|||||txtccrThe rational function analogue of a question of Schur and exceptionality of permutation representations /Robert M. Guralnick, Peter Müller, Jan SaxlProvidence, Rhode Island :American Mathematical Society,2003.1 online resource (96 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 773"Volume 162, number 773 (end of volume)."0-8218-3288-3 Includes bibliographical references.""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""""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""Memoirs of the American Mathematical Society ;no. 773.Algebraic fieldsArithmetic functionsPermutation groupsPolynomialsElectronic books.Algebraic fields.Arithmetic functions.Permutation groups.Polynomials.512/.3Guralnick Robert M.1950-871746Müller Peter1966-Saxl J(Jan),1948-MiAaPQMiAaPQMiAaPQBOOK9910480222903321The rational function analogue of a question of Schur and exceptionality of permutation representations1945841UNINA