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A remark on multivalued algebraic groups

Author: Anand Pillay
Journal: Proc. Amer. Math. Soc. 137 (2009), 2175-2180
MSC (2000): Primary 14L10; Secondary 03C45
Published electronically: December 18, 2008
MathSciNet review: 2495249
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Abstract: We point out how suitable algebraic $ n$-valued groups (in the sense of Buchstaber) give rise, in a reasonably canonical manner, to algebraic groups. This is proved using the ``group configuration theorem'' of Hrushovski. In particular this applies to all algebraic $ 2$-valued groups.

References [Enhancements On Off] (What's this?)

  • 1. Victor M. Buchstaber, 𝑛-valued groups: theory and applications, Mosc. Math. J. 6 (2006), no. 1, 57–84, 221 (English, with English and Russian summaries). MR 2265947
  • 2. Anand Pillay, Geometric stability theory, Oxford Logic Guides, vol. 32, The Clarendon Press, Oxford University Press, New York, 1996. Oxford Science Publications. MR 1429864

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Additional Information

Anand Pillay
Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

Received by editor(s): December 25, 2007
Received by editor(s) in revised form: July 22, 2008, and August 29, 2008
Published electronically: December 18, 2008
Additional Notes: The author was supported by a Marie Curie Chair EXC 024052 as well as EPSRC grant EP/F009712/1
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.