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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On genericity and weight in the free group


Author: Anand Pillay
Journal: Proc. Amer. Math. Soc. 137 (2009), 3911-3917
MSC (2000): Primary 03C45; Secondary 20F67
Published electronically: June 18, 2009
MathSciNet review: 2529900
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Abstract: We prove that the generic type of the (theory of the) free group $ F_{n}$ on $ n\geq 2$ generators has infinite weight, strengthening the well-known result that these free groups are not superstable. A preliminary result, possibly of independent interest, is that the realizations in $ F_{n}$ of the generic type are precisely the primitives.


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Additional Information

Anand Pillay
Affiliation: School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom
Email: pillay@maths.leeds.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09956-0
PII: S 0002-9939(09)09956-0
Received by editor(s): December 9, 2008
Received by editor(s) in revised form: March 3, 2009
Published electronically: June 18, 2009
Additional Notes: This work was supported by Marie Curie Chair EXC 024052 as well as EPSRC grant EP/F009712/1
Communicated by: Julia Knight
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.