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ON MAXIMAL STABLE QUOTIENTS OF DEFINABLE GROUPS IN NIP THEORIES

Published online by Cambridge University Press:  08 February 2018

MIKE HASKEL  and
ANAND PILLAY
MIKE HASKEL
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NOTRE DAME NOTRE DAME, IN 46556, USA E-mail: mike.haskel@gmail.com
ANAND PILLAY
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NOTRE DAME NOTRE DAME, IN 46556, USA E-mail: apillay@nd.edu
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Abstract

For G a group definable in a saturated model of a NIP theory T, we prove that there is a smallest type-definable subgroup H of G such that the quotient G / H is stable. This generalizes the existence of G00, the smallest type-definable subgroup of G of bounded index.

Keywords

03C4503C60stabilityNIPhyperdefinabilitydefinable groups

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 117 - 122
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

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