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Approximate subgroups. (English. French summary) Zbl 1379.03008
Summary: Given a definably amenable approximate subgroup $$A$$ of a (local) group in some first-order structure, there is a type-definable subgroup $$H$$ normalized by $$A$$ and contained in $$A^4$$ such that every definable superset of $$H$$ has positive measure.

##### MSC:
 03C60 Model-theoretic algebra 20F99 Special aspects of infinite or finite groups 03C50 Models with special properties (saturated, rigid, etc.) 03C40 Interpolation, preservation, definability 20A15 Applications of logic to group theory 20E07 Subgroup theorems; subgroup growth 03C98 Applications of model theory
##### Keywords:
approximate subgroup; definability; definable amenability
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##### References:
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