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On the linearity of torsion-free nilpotent groups of finite Morley rank
Author(s):
Tuna
Altinel;
John
S.
Wilson
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1813-1821.
MSC (2000):
Primary 03C60, 20F16
Posted:
December 15, 2008
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Abstract:
It is proved that every torsion-free nilpotent group of finite Morley rank is isomorphic to a matrix group over a field of characteristic zero.
References:
-
- 1.
- I. D. Ado. The representation of Lie algebras by matrices. Uspehi Mat. Nauk. (N.S.) 2 (1947), no. 6 (22), 159-173. (A.M.S Transl. No. 2 (1949)) MR 0027753 (10:350c)
- 2.
- A. Baudisch. A new uncountably categorical group. Trans. Amer. Math. Soc. 348 (1996), 3889-3940. MR 1351488 (96m:03020)
- 3.
- A. V. Borovik and A. Nesin. Groups of Finite Morley Rank. Oxford University Press, 1994. MR 1321141 (96c:20004)
- 4.
- G. Cherlin and J. Reineke.
Categoricity and stability of commutative rings. Ann. Math. Logic 10 (1976), 367-399. MR 0480007 (58:208) - 5.
- I. S. Cohen. On the structure and ideal theory of complete local rings. Trans. Amer. Math. Soc. 59 (1946), 54-106. MR 0016094 (7:509h)
- 6.
- O. Frécon. Linearity of solvable groups of finite Morley rank. Preprint, 2007.
- 7.
- W. Hodges. Model Theory. Encyclopedia of Mathematics and its Applications 42. Cambridge University Press, 1993. MR 1221741 (94e:03002)
- 8.
- N. Jacobson. Lie Algebras. Dover Publications, 1962. MR 0143793 (26:1345)
- 9.
- N. Jacobson. Basic Algebra II. W. H. Freeman and Company, 1989. MR 1009787 (90m:00007)
- 10.
- A. Macintyre. On
-categorical theories of fields. Fund. Math. 71 (1971), 1-25. MR 0290954 (45:48) - 11.
- A. Nesin. Non-associative rings of finite Morley rank. In The Model Theory of Groups, edited by A. Nesin and A. Pillay, Notre Dame Mathematical Lectures 11, Notre Dame Press, 1989, 117-137. MR 985343
- 12.
- I. Stewart. An algebraic treatment of Malcev's theorem concerning nilpotent Lie groups and their Lie algebras. Compositio Math. 22 (1970), 289-312. MR 0288158 (44:5356)
- 13.
- R. B. Warfield Jr. Nilpotent Groups. Lecture Notes in Math. 513. Springer-Verlag, 1976. MR 0409661 (53:13413)
- 14.
- B. I. Zil'ber. Rings with
-categorical theories. Algebra and Logic 13 (1974), 95-104. (Translation from Algebra i Logika 13, No. 2 (1974), 168-187.) MR 0366650 (51:2897)
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Additional Information:
Tuna
Altinel
Affiliation:
Université de Lyon, Université Lyon 1, CNRS UMR 5208 Institut Camille Jordan, INSA de Lyon, F-69621, Ecole Centrale de Lyon, 43 blvd du 11 novembre 1918, 69622 Villeurbanne cedex, France
Email:
altinel@math.univ-lyon1.fr
John
S.
Wilson
Affiliation:
University College, Oxford OX1 4BH, United Kingdom
Email:
wilsonjs@maths.ox.ac.uk
DOI:
10.1090/S0002-9939-08-09695-0
PII:
S 0002-9939(08)09695-0
Received by editor(s):
March 3, 2008,
Received by editor(s) in revised form:
July 9, 2008
Posted:
December 15, 2008
Additional Notes:
The first author was supported by MODNET, an FP6 Marie Curie Research Training Network in Model Theory and its Applications, funded by the European Commission under contract number MRTN-CT-2004-512234 (MODNET)
Communicated by:
Julia Knight
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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