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Available in print format 		Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Book Review

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Book Information

Author(s): 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

References:

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[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.

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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)

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J.-F. Mestre, Extensions régulières de $ \mathbb{Q}(T)$ de groupe de Galois $ {\tilde A_n}$, 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).

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-, Conversation at Walter Feit's birthday celebration at Oxford in April 1990.

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I. R. Shafarevich, The embedding problem for split extensions, Dokl. Akad. Nauk SSSR 120 (1958), 1217-1219. MR 0102509 (21:1301)

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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 $ {\text{Gal}}(L/K)$, where $ K\, \subseteq \, \mathbb{Q}({\mu _n})$, J. Algebra 89 (1984), 437-499. MR 751155 (87f:12012)

[V1]
H. Völklein, $ {\text{G}}{{\text{L}}_n}(q)$ 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 $ {\text{PGL}}_{n}(q)$, $ {\text{PU}}_{n}({q^2})$, Forum Math. (1994) (to appear).

Additional Information:

Reviewer(s):
Michael Fried

Review Information:
Journal: Bull. Amer. Math. Soc. 30 (1994), 124-135.
DOI: 10.1090/S0273-0979-1994-00445-8
PII: S 0273-0979(1994)00445-8




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