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In the introduction the author tries to give an intuitive description of the lemma by saying that the points around a small neighbourhood are in the orbit of (a finite amount of) nilpotent groups. While this image is evocative, it is in fact wrong, as the theorem says that the points are in the orbit of a virtually nilpotent group. While a vitually nilpotent group is indeed covered by a finite amount of translations of a nilpotent subgroup, its elements need not to be contained in a nilpotent group. 31.191.173.68 ( talk) 16:58, 20 January 2023 (UTC)
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In the introduction the author tries to give an intuitive description of the lemma by saying that the points around a small neighbourhood are in the orbit of (a finite amount of) nilpotent groups. While this image is evocative, it is in fact wrong, as the theorem says that the points are in the orbit of a virtually nilpotent group. While a vitually nilpotent group is indeed covered by a finite amount of translations of a nilpotent subgroup, its elements need not to be contained in a nilpotent group. 31.191.173.68 ( talk) 16:58, 20 January 2023 (UTC)