The paper shows a radical relationship between local nilpotency and local finiteness in homogeneous varieties, implying their interdependence.
In this paper, we prove that in a homogeneous variety [Formula: see text] one of the properties of local nilpotency and of local finiteness is radical in the sense of Amitsur-Kurosh if and only of so is the second property.
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Ivan Shestakov (2026) studied this question.
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