Abstract
Let $V$ be an infinite-dimensional vector space over any division ring $D$, and let $G$ be an irreducible primitive subgroup of the finitary group $\mathrm {FGL} (V)$. We prove that every non-identity ascendant subgroup of $G$ is also irreducible and primitive. For $D$ a field, this was proved earlier by U. Meierfrankenfeld.
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