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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
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