Book Review
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MathSciNet review:
1568073
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Book Information:
Author:
J.-P. Serre
Title:
Topics in Galois Theory
Additional book information:
Research Notes in Mathematics, 1992, Jones and Bartlett Publishers, xvi+116 pp. ISBN 0-86720-210-6.
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, $\Bbb {ATLAS}$ of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups; With computational assistance from J. G. Thackray. MR 827219
G. V. Belyĭ, On extensions of the maximal cyclotomic field having a given classical Galois group, J. Reine Angew. Math. 341 (1983), 147–156. MR 697314, DOI 10.1515/crll.1983.341.147
[DFr] P. Debes and M. Fried, Nonrigid situations in constructive Galois theory, Pacific J. Math. (1993), in proof August 1993.
M. Fried, Fields of definition of function fields and Hurwitz families—groups as Galois groups, Comm. Algebra 5 (1977), no. 1, 17–82. MR 453746, DOI 10.1080/00927877708822158
Michael D. Fried and Moshe Jarden, Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 11, Springer-Verlag, Berlin, 1986. MR 868860, DOI 10.1007/978-3-662-07216-5
Michael D. Fried and Helmut Völklein, The inverse Galois problem and rational points on moduli spaces, Math. Ann. 290 (1991), no. 4, 771–800. MR 1119950, DOI 10.1007/BF01459271
[FrV2] -, The embedding problem over an Hilbertian-PAC field, Ann. of Math. (2) 135 (1992), 1-13.
S. Kamienny and B. Mazur, Rational torsion of prime order in elliptic curves over number fields, Astérisque 228 (1995), 3, 81–100. With an appendix by A. Granville; Columbia University Number Theory Seminar (New York, 1992). MR 1330929
Nicholas M. Katz and Serge Lang, Finiteness theorems in geometric classfield theory, Enseign. Math. (2) 27 (1981), no. 3-4, 285–319 (1982). With an appendix by Kenneth A. Ribet. MR 659153
B. Mazur, Rational points on modular curves, Modular functions of one variable, V (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976) Lecture Notes in Math., Vol. 601, Springer, Berlin, 1977, pp. 107–148. MR 0450283
B. Heinrich Matzat, Konstruktive Galoistheorie, Lecture Notes in Mathematics, vol. 1284, Springer-Verlag, Berlin, 1987 (German). MR 1004467, DOI 10.1007/BFb0098324
Gunter Malle, Exceptional groups of Lie type as Galois groups, J. Reine Angew. Math. 392 (1988), 70–109. MR 965058, DOI 10.1515/crll.1988.392.70
Jean-François Mestre, Extensions régulières de $\textbf {Q}(T)$ de groupe de Galois $\~A_n$, J. Algebra 131 (1990), no. 2, 483–495 (French). MR 1058560, DOI 10.1016/0021-8693(90)90189-U
Jean-Pierre Serre, Topics in Galois theory, Research Notes in Mathematics, vol. 1, Jones and Bartlett Publishers, Boston, MA, 1992. Lecture notes prepared by Henri Damon [Henri Darmon]; With a foreword by Darmon and the author. MR 1162313
[Se2] -, Points rationnels des courbes modulaires, Sém. Bourbaki, 30ème année no. 511 (1977/78).
[Se3] -, Conversation at Walter Feit's birthday celebration at Oxford in April 1990.
I. R. Šafarevič, The imbedding problem for splitting extensions, Dokl. Akad. Nauk SSSR 120 (1958), 1217–1219 (Russian). MR 0102509
Kuang-yen Shih, On the construction of Galois extensions of function fields and number fields, Math. Ann. 207 (1974), 99–120. MR 332725, DOI 10.1007/BF01362150
John G. Thompson, Some finite groups which appear as $\textrm {Gal}\,L/K$, where $K\subseteq \textbf {Q}(\mu _{n})$, J. Algebra 89 (1984), no. 2, 437–499. MR 751155, DOI 10.1016/0021-8693(84)90228-X
Helmut Völklein, $\textrm {GL}_n(q)$ as Galois group over the rationals, Math. Ann. 293 (1992), no. 1, 163–176. MR 1162680, DOI 10.1007/BF01444710
[V2] -, Braid group action, embedding problems and the groups , , Forum Math. (1994) (to appear).
- [At]
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of finite groups: maximal subgroups and ordinary characters for simple groups, Clarendon Press, New York, 1985. MR 827219 (88g:20025)
- [B]
- G. V. Belyi, On extensions of the maximal cyclotomic field having a given classical group, J. Crelle341 (1983), 147-156. MR 697314 (84h:12010)
- [DFr]
- P. Debes and M. Fried, Nonrigid situations in constructive Galois theory, Pacific J. Math. (1993), in proof August 1993.
- [Fr]
- M. Fried, Fields of definition of function fields and Hurwitz families and Groups as Galois groups, Comm. Algebra 5 (1977), 17-82. MR 0453746 (56:12006)
- [FrJ]
- M. Fried and M. Jarden, Field arithmetic, Ergeb. Math. Grenzgeb., vol. 11, Springer-Verlag, Berlin and New York, 1986. MR 868860 (89b:12010)
- [FrV]
- M. Fried and H. Völklein, The inverse Galois problem and rational points on moduli spaces, Math. Ann. 290 (1991), 771-800. MR 1119950 (93a:12004)
- [FrV2]
- -, The embedding problem over an Hilbertian-PAC field, Ann. of Math. (2) 135 (1992), 1-13.
- [KM]
- S. Kamienny and B. Mazur, Rational torsion of prime order in elliptic curves over number fields, Columbia University Number Theory Seminar, 1992, Astérisque (to appear). MR 1330929 (96c:11058)
- [KL]
- N. Katz and S. Lang, Torsion points on abelian varieties in cyclotomic extensions (Appendix by K. Ribet), Enseign. Math. 27 (1981). MR 659153 (83k:14012)
- [M]
- B. Mazur, Rational points on modular curves, Lecture Notes in Math., vol. 601, Springer, New York, 1977, pp. 107-148. MR 0450283 (56:8579)
- [Ma]
- B. H. Matzat, Konstructive Galoistheorie, Lecture Notes in Math., vol. 1284, Springer, New York, 1987. MR 1004467 (91a:12007)
- [Ma1]
- G. Malle, Exceptional groups of Lie type as Galois groups, J. Crelle 392 (1988), 70-109. MR 965058 (89m:12004)
- [Me]
- J.-F. Mestre, Extensions régulières de de groupe de Galois , J. Algebra 131 (1990), 483-495. MR 1058560 (91j:12010)
- [Se]
- J.-P. Serre, Topics in Galois theory, Res. Notes in Math., vol. 1, Jones and Bartlett, Boston and London, 1992. MR 1162313 (94d:12006)
- [Se2]
- -, Points rationnels des courbes modulaires, Sém. Bourbaki, 30ème année no. 511 (1977/78).
- [Se3]
- -, Conversation at Walter Feit's birthday celebration at Oxford in April 1990.
- [Sh]
- I. R. Shafarevich, The embedding problem for split extensions, Dokl. Akad. Nauk SSSR 120 (1958), 1217-1219. MR 0102509 (21:1301)
- [S]
- K. Shih, On the construction of Galois extensions of function fields and number fields, Math. Ann. 207 (1974), 99-120. MR 0332725 (48:11051)
- [Th]
- J. G. Thompson, Some finite groups which appear as , where , J. Algebra 89 (1984), 437-499. MR 751155 (87f:12012)
- [V1]
- H. Völklein, as Galois group over the rationals, Math. Ann. 293 (1992), 163-176. MR 1162680 (94a:12007)
- [V2]
- -, Braid group action, embedding problems and the groups , , Forum Math. (1994) (to appear).
Review Information:
Reviewer:
Michael Fried
Journal:
Bull. Amer. Math. Soc.
30 (1994), 124-135
DOI:
https://doi.org/10.1090/S0273-0979-1994-00445-8