Book Review
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Book Information:
Authors:
G. Malle and
B. H. Matzat
Title:
Inverse Galois theory
Additional book information:
Springer-Verlag, Berlin, Heidelberg, New York,
1999,
xv + 436 pp.,
ISBN 3-540-62890-8,
$59.95$
[A] S.S. ABHYANKAR, Further nice equations for nice groups, Transactions AMS 348 (1996), 1555-1577. MR 1348146
[Be] G.V. BELYI, On extensions of the maximal cyclotomic field having a given classical Galois group, J. reine angew. Math. 341 (1983), 147-156. MR 0697314
[DR1] M. DETTWEILER AND S. REITER, On rigid tuples in linear groups of odd dimension, J. Algebra 222 (1999), 550-560. CMP 2000:07
[DR2] M. DETTWEILER AND S. REITER, An algorithm of Katz and its application in Galois Theory, preprint 1999.
[Fr] M. FRIED, Fields of definition of function fields and Hurwitz families -- groups as Galois groups, Comm. Algebra 5 (1977), 17-82. MR 0453746
[FJ] M. FRIED AND M. JARDEN, Field Arithmetic, Ergebn. Math. und Ihrer Grenzgeb. 11, Springer Verlag 1986. MR 0868860
[FV1] M. FRIED AND H. V¨OLKLEIN, The inverse Galois problem and rational points on moduli spaces, Math. Annalen 290 (1991), 771-800. MR 1119950
[FV2] M. FRIED AND H. V¨OLKLEIN, The embedding problem over a Hilbertian PAC-field, Annals of Math. 135 (1992), 469-481. MR 1166641
[FM] D. FROHARDT AND K. MAGAARD, Composition factors of monodromy groups, to appear in Annals of Math.
[GT] R.M. GURALNICK AND J.G. THOMPSON, Finite groups of genus zero, J. Algebra 131 (1990), 303 - 341. MR 1055011
[Har] D. HARAN, Hilbertian fields under separable algebraic extensions, Invent. Math. 137 (1999), 113-126. CMP 99:16
[HJ] D. HARAN AND M. JARDEN, The absolute Galois group of , to appear in Pacific J. Math.
[Ha] D. HARBATER, Abhyankar's Conjecture on Galois Groups over Curves, Invent. Math. 117 (1994), 1-25. MR 1269423
[Hur] A. HURWITZ, Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten, Math. Annalen 39 (1891), 1-61.
[Ka] N. KATZ, Rigid local systems, Princeton University Press, 1996. MR 1366651
[Malle] G. MALLE, Exceptional groups of Lie type as Galois groups, J. reine angew. Math. 392 (1988), 70-109. MR 0965058
[Mat1] B. H. MATZAT, Konstruktive Galoistheorie, Lect. Notes in Math. 1284, Springer, Heidelberg, 1987. MR 1004467
[Mat2] B. H. MATZAT, Zum Einbettungsproblem der algebraischen Zahlentheorie mit nicht-abelschem Kern, Invent. Math. 80 (1985), 365-374. MR 0788415
[Mat3] B. H. MATZAT, Zöpfe und Galoissche Gruppen, J. reine angew. Math. 420 (1991), 99-159. MR 1124568
[Ra] M. RAYNAUD, Revêtements de la droite affine en caractéristique et conjecture d'Abhyankar, Invent. Math. 116 (1994), 425-462. MR 1253200
[Se] J.-P. SERRE, Topics in Galois Theory, Jones and Bartlett, Boston, 1992. MR 1162313
[SV] K. STRAMBACH AND H. V¨OLKLEIN, On linearly rigid tuples, J. reine angew. Math. 510 (1999), 57-62. MR 1696090
[Th1] J. G. THOMPSON, Some finite groups which appear as , where , J. Algebra 89 (1984), 437-499. MR 0751155
[Th2] J. G. THOMPSON, Rigidity, GL, and the braid group, Bull. Soc. Math. Belg. 17 (1990), 723-733. MR 1316220
[ThV1] J. THOMPSON AND H. V¨OLKLEIN, Symplectic groups as Galois groups, J. Group Theory 1 (1998), 1-58. MR 1490157
[ThV2] J. THOMPSON AND H. V¨OLKLEIN, Braid-abelian tuples in , pp. 218-238 in: Aspects of Galois Theory, London Math. Soc. Lect. Notes 256, Cambridge University Press 1999. MR 1708608
[V1] H. V¨OLKLEIN, Groups as Galois Groups - an Introduction, Cambr. Studies in Adv. Math. 53, Cambridge Univ. Press 1996. MR 1405612
[V2] H. V¨OLKLEIN, Rigid generators of classical groups, Math. Annalen 311 (1998), 421-438. MR 1637911
[V3] H. V¨OLKLEIN, The braid group and linear rigidity, to appear in Geom. Ded.
[V4] H. V¨OLKLEIN, A transformation principle for covers of , to appear in J. reine angew. Math.
- [A]
- S.S. ABHYANKAR, Further nice equations for nice groups, Transactions AMS 348 (1996), 1555-1577. MR 1348146
- [Be]
- G.V. BELYI, On extensions of the maximal cyclotomic field having a given classical Galois group, J. reine angew. Math. 341 (1983), 147-156. MR 0697314
- [DR1]
- M. DETTWEILER AND S. REITER, On rigid tuples in linear groups of odd dimension, J. Algebra 222 (1999), 550-560. CMP 2000:07
- [DR2]
- M. DETTWEILER AND S. REITER, An algorithm of Katz and its application in Galois Theory, preprint 1999.
- [Fr]
- M. FRIED, Fields of definition of function fields and Hurwitz families -- groups as Galois groups, Comm. Algebra 5 (1977), 17-82. MR 0453746
- [FJ]
- M. FRIED AND M. JARDEN, Field Arithmetic, Ergebn. Math. und Ihrer Grenzgeb. 11, Springer Verlag 1986. MR 0868860
- [FV1]
- M. FRIED AND H. V¨OLKLEIN, The inverse Galois problem and rational points on moduli spaces, Math. Annalen 290 (1991), 771-800. MR 1119950
- [FV2]
- M. FRIED AND H. V¨OLKLEIN, The embedding problem over a Hilbertian PAC-field, Annals of Math. 135 (1992), 469-481. MR 1166641
- [FM]
- D. FROHARDT AND K. MAGAARD, Composition factors of monodromy groups, to appear in Annals of Math.
- [GT]
- R.M. GURALNICK AND J.G. THOMPSON, Finite groups of genus zero, J. Algebra 131 (1990), 303 - 341. MR 1055011
- [Har]
- D. HARAN, Hilbertian fields under separable algebraic extensions, Invent. Math. 137 (1999), 113-126. CMP 99:16
- [HJ]
- D. HARAN AND M. JARDEN, The absolute Galois group of , to appear in Pacific J. Math.
- [Ha]
- D. HARBATER, Abhyankar's Conjecture on Galois Groups over Curves, Invent. Math. 117 (1994), 1-25. MR 1269423
- [Hur]
- A. HURWITZ, Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten, Math. Annalen 39 (1891), 1-61.
- [Ka]
- N. KATZ, Rigid local systems, Princeton University Press, 1996. MR 1366651
- [Malle]
- G. MALLE, Exceptional groups of Lie type as Galois groups, J. reine angew. Math. 392 (1988), 70-109. MR 0965058
- [Mat1]
- B. H. MATZAT, Konstruktive Galoistheorie, Lect. Notes in Math. 1284, Springer, Heidelberg, 1987. MR 1004467
- [Mat2]
- B. H. MATZAT, Zum Einbettungsproblem der algebraischen Zahlentheorie mit nicht-abelschem Kern, Invent. Math. 80 (1985), 365-374. MR 0788415
- [Mat3]
- B. H. MATZAT, Zöpfe und Galoissche Gruppen, J. reine angew. Math. 420 (1991), 99-159. MR 1124568
- [Ra]
- M. RAYNAUD, Revêtements de la droite affine en caractéristique et conjecture d'Abhyankar, Invent. Math. 116 (1994), 425-462. MR 1253200
- [Se]
- J.-P. SERRE, Topics in Galois Theory, Jones and Bartlett, Boston, 1992. MR 1162313
- [SV]
- K. STRAMBACH AND H. V¨OLKLEIN, On linearly rigid tuples, J. reine angew. Math. 510 (1999), 57-62. MR 1696090
- [Th1]
- J. G. THOMPSON, Some finite groups which appear as , where , J. Algebra 89 (1984), 437-499. MR 0751155
- [Th2]
- J. G. THOMPSON, Rigidity, GL, and the braid group, Bull. Soc. Math. Belg. 17 (1990), 723-733. MR 1316220
- [ThV1]
- J. THOMPSON AND H. V¨OLKLEIN, Symplectic groups as Galois groups, J. Group Theory 1 (1998), 1-58. MR 1490157
- [ThV2]
- J. THOMPSON AND H. V¨OLKLEIN, Braid-abelian tuples in , pp. 218-238 in: Aspects of Galois Theory, London Math. Soc. Lect. Notes 256, Cambridge University Press 1999. MR 1708608
- [V1]
- H. V¨OLKLEIN, Groups as Galois Groups - an Introduction, Cambr. Studies in Adv. Math. 53, Cambridge Univ. Press 1996. MR 1405612
- [V2]
- H. V¨OLKLEIN, Rigid generators of classical groups, Math. Annalen 311 (1998), 421-438. MR 1637911
- [V3]
- H. V¨OLKLEIN, The braid group and linear rigidity, to appear in Geom. Ded.
- [V4]
- H. V¨OLKLEIN, A transformation principle for covers of , to appear in J. reine angew. Math.
Review Information:
Reviewer:
Helmut Völklein
Affiliation:
University of Florida
Email:
helmut@math.ufl.edu
Journal:
Bull. Amer. Math. Soc.
38 (2001), 235-243
Published electronically:
December 27, 2000
Review copyright:
© Copyright 2000
American Mathematical Society