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December 2005 Subsimple groups
Frank Wagner
J. Symbolic Logic 70(4): 1365-1370 (December 2005). DOI: 10.2178/jsl/1129642130

Abstract

We define a notion of genericity for arbitrary subgroups of groups interpretable in a simple theory, and show that a type generic for such a group is generic for the minimal hyperdefinable supergroup (the definable hull). In particular, at least one generic type of the definable hull is finitely satisfiable in the original subgroup. If the subgroup is a subfield, then the additive and the multiplicative definable hull both have bounded index in the smallest hyperdefinable superfield.

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Frank Wagner. "Subsimple groups." J. Symbolic Logic 70 (4) 1365 - 1370, December 2005. https://doi.org/10.2178/jsl/1129642130

Information

Published: December 2005
First available in Project Euclid: 18 October 2005

zbMATH: 1104.03025
MathSciNet: MR2194252
Digital Object Identifier: 10.2178/jsl/1129642130

Subjects:
Primary: 03C45

Keywords: generic , simple field , simplicity , subgroup

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 4 • December 2005
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