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THE RIGHT ANGLE TO LOOK AT ORTHOGONAL SETS

Published online by Cambridge University Press:  29 September 2016

FRANK O. WAGNER
FRANK O. WAGNER*
Affiliation:
UNIVERSITÉ DE LYON; CNRS UNIVERSITÉ CLAUDE BERNARD LYON 1 INSTITUT CAMILLE JORDAN UMR 5208 43 BD DU 11 NOVEMBRE 1918 69622 VILLEURBANNE CEDEX, FRANCE E-mail: [email protected]
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Abstract

If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in X ∪ Y has a normal hyperdefinable X-internal subgroup N such that G/N is Y-internal; N is unique up to commensurability. In order to make sense of this statement, local simplicity theory for hyperdefinable sets is developed. Moreover, a version of Schlichting’s Theorem for hyperdefinable families of commensurable subgroups is shown.

Keywords

03C45orthogonalitysimplicityinternality
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 4 , December 2016 , pp. 1298 - 1314
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

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