Book Review
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MathSciNet review:
2721046
Full text of review:
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Book Information:
Authors:
T. Altinel,
A. V. Borovik and
G. Cherlin
Title:
Simple groups of finite Morley rank
Additional book information:
Mathematical Surveys and Monographs, 145,
American Mathematical Society, Providence, RI,
2008,
xix+556 pp.,
ISBN 978-0-8218-4305-5,
US $109.00
J. T. Baldwin and A. H. Lachlan, On strongly minimal sets, J. Symbolic Logic 36 (1971), 79–96. MR 286642, DOI 10.2307/2271517
J. T. Baldwin and Jan Saxl, Logical stability in group theory, J. Austral. Math. Soc. Ser. A 21 (1976), no. 3, 267–276. MR 407151, DOI 10.1017/s1446788700018553
Aleksandr Vasilievich Borovik and Bruno Petrovich Poizat, Tores et $p$-groupes, J. Symbolic Logic 55 (1990), no. 2, 478–491 (French). MR 1056365, DOI 10.2307/2274641
Alexandre Borovik and Ali Nesin, Groups of finite Morley rank, Oxford Logic Guides, vol. 26, The Clarendon Press, Oxford University Press, New York, 1994. Oxford Science Publications. MR 1321141
Gregory Cherlin, Groups of small Morley rank, Ann. Math. Logic 17 (1979), no. 1-2, 1–28. MR 552414, DOI 10.1016/0003-4843(79)90019-6
Ehud Hrushovski, A new strongly minimal set, Ann. Pure Appl. Logic 62 (1993), no. 2, 147–166. Stability in model theory, III (Trento, 1991). MR 1226304, DOI 10.1016/0168-0072(93)90171-9
Linus Kramer, Katrin Tent, and Hendrik Van Maldeghem, Simple groups of finite Morley rank and Tits buildings, Israel J. Math. 109 (1999), 189–224. MR 1679598, DOI 10.1007/BF02775036
Michael Morley, Categoricity in power, Trans. Amer. Math. Soc. 114 (1965), 514–538. MR 175782, DOI 10.1090/S0002-9947-1965-0175782-0
Bruno Poizat, Groupes stables, Nur al-Mantiq wal-Maʾrifah [Light of Logic and Knowledge], vol. 2, Bruno Poizat, Lyon, 1987 (French). Une tentative de conciliation entre la géométrie algébrique et la logique mathématique. [An attempt at reconciling algebraic geometry and mathematical logic]. MR 902156
Frank O. Wagner, Stable groups, London Mathematical Society Lecture Note Series, vol. 240, Cambridge University Press, Cambridge, 1997. MR 1473226, DOI 10.1017/CBO9780511566080
References
- J.T. Baldwin, A.H. Lachlan, On strongly minimal sets, J. Symb. Logic 36 (1971), 79–96. MR 0286642 (44:3851)
- J.T. Baldwin, J. Saxl, Logical stability in group theory, J. Austral. Math. Soc. Ser. A 21 (1976), 267–276. MR 0407151 (53:10934)
- A. Borovik, B. Poizat, Tores et $p$-groupes, J. Symb. Logic 55 (1990), 565–583. MR 1056365 (91j:03045)
- A. Borovik, A. Nesin, Groups of finite Morley rank, Clarendon Press, Oxford, 1994. MR 1321141 (96c:20004)
- G. Cherlin, Groups of small Morley rank, Ann. Math. Logic 17 (1979), 1–28. MR 552414 (81h:03072)
- E. Hrushovski, A new strongly minimal set, Ann. Pure Appl. Logic 62 (1993), 147–166. MR 1226304 (94d:03064)
- L. Kramer, K. Tent, H. van Maldeghem, Simple groups of finite Morley rank and Tits buildings, Isr. J. Math. 109 (1999), 189–224. MR 1679598 (2000f:51022)
- M. Morley, Categoricity in power, Trans. Amer. Math. Soc. 114 (1965), 514–538. MR 0175782 (31:58)
- B. Poizat, Groupes stables, Nur Al-Mantiq Wal-Ma’rifah, Villeurbanne, France, 1987. English translation in 2001 (Mathematical Surveys and Monographs 87, American Mathematical Society, RI). MR 902156 (89b:03056)
- F. Wagner, Stable groups, London Math Soc. Lecture Notes 240, Cambridge University Press, Cambridge, 1997. MR 1473226 (99g:20010)
Review Information:
Reviewer:
Dugald Macpherson
Affiliation:
University of Leeds
Email:
h.d.macpherson@leeds.ac.uk
Journal:
Bull. Amer. Math. Soc.
47 (2010), 729-734
DOI:
https://doi.org/10.1090/S0273-0979-10-01287-5
Published electronically:
February 24, 2010
Review copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
