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.

*$\Bbb {ATLAS}$ 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**

*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]**

*Nonrigid situations in constructive Galois theory*, Pacific J. Math. (1993), in proof August 1993.

*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

*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

*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.

*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**

*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**

*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**

*Konstruktive Galoistheorie*, Lecture Notes in Mathematics, vol. 1284, Springer-Verlag, Berlin, 1987 (German). MR

**1004467**, DOI 10.1007/BFb0098324

*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

*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

*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]**

*The imbedding problem for splitting extensions*, Dokl. Akad. Nauk SSSR

**120**(1958), 1217–1219 (Russian). MR

**0102509**

*On the construction of Galois extensions of function fields and number fields*, Math. Ann.

**207**(1974), 99–120. MR

**332725**, DOI 10.1007/BF01362150

*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

*$\textrm {GL}_n(q)$ 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).

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