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19.106 (2018)

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Let $G$ be a uniformly locally finite group (which means that there is a function $f$ on the natural numbers such that any subgroup generated by $n$ elements has size at most $f(n)$). Suppose that for any two definable subgroups $H$ and $K$, the intersection $H \cap K$ has finite index either in $H$ or in $K$. Is $G$ necessarily nilpotent-by-finite? Or even finite-by-abelian-by-finite?

Contributor: F. Wagner

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