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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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- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of finite groups\,\RM : maximal subgroups and ordinary characters for simple groups, Clarendon Press, New York, 1985.
- [B]
- G. V. Belyi, On extensions of the maximal cyclotomic field having a given classical group, J. Crelle \textbf{341} (1983), 147--156.
- [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 {\rm and} Groups as Galois groups, Comm. Algebra \textbf{5} (1977), 17--82.
- [FrJ]
- M. Fried and M. Jarden, Field arithmetic, Ergeb. Math. Grenzgeb., vol. 11, Springer-Verlag, Berlin and New York, 1986.
- [FrV]
- M. Fried and H. V\"olklein, The inverse Galois problem and rational points on moduli spaces, Math. Ann. \textbf{290} (1991), 771--800.
- [FrV2]
- M. Fried and H. V\"olklein, The embedding problem over an Hilbertian-PAC field, Ann. of Math. (2) \textbf{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, Ast\'erisque.
- [KL]
- N. Katz and S. Lang, Torsion points on abelian varieties in cyclotomic extensions {\rm (Appendix by K. Ribet)}, Enseign. Math. \textbf{27} (1981).
- [M]
- B. Mazur, \emph{Rational points on modular curves} vol.~601, Springer, New York, 1977 pp.~107--148.
- [Ma]
- B. H. Matzat, \emph{Konstructive Galoistheorie}, . Springer, New York, 1987.
- [Ma1]
- G. Malle, Exceptional groups of Lie type as Galois groups, J. Crelle \textbf{392} (1988), 70--109.
- [Me]
- J.-F. Mestre, Extensions r\'eguli\`eres de $\Bbb Q(T)$ de groupe de Galois $\widetilde A_n$, J. Algebra \textbf{131} (1990), 483--495.
- [Se]
- J.-P. Serre, Topics in Galois theory, Res. Notes in Math., vol.~1, Jones and Bartlett, Boston and London, 1992.
- [Se2]
- J.-P. Serre, Points rationnels des courbes modulaires, S\'em. Bourbaki, 30\`eme ann\'ee no. 511 (1977/78).
- [Se3]
- J.-P. Serre, 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 \textbf{120} (1958), 1217--1219.
- [S]
- K. Shih, On the construction of Galois extensions of function fields and number fields, Math. Ann. \textbf{207} (1974), 99--120.
- [Th]
- J. G. Thompson, Some finite groups which appear as $\operatorname {Gal}(L/K)$, where $K\subseteq \Bbb Q(\mu _n)$, J. Algebra \textbf{89} (1984), 437--499.
- [V1]
- H. V\"olklein, $\operatorname {GL}_n(q)$ as Galois group over the rationals, Math. Ann. \textbf{293} (1992), 163--176.
- [V2]
- H. V\"olklein, Braid group action, embedding problems and the groups $\operatorname {PGL}_n(q)$, $\operatorname {PU}_n(q^2)$, 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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