Geodesic
On the closedness of carpets of additive subgroups associated with a Chevalley group over a commutative ring
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 6, pp. 732-737

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Let $\mathfrak{A}=\{\mathfrak{A}_r\ |\ r\in \Phi\}$ be a carpet of additive subgroups of type $\Phi$ over an arbitrary commutative ring $K$. A sufficient condition for the carpet $\mathfrak{A}$ to be closed is established. As a corollary, we obtain a positive answer to question 19.63 from the Kourovka notebook and a confirmation of one conjecture by V. M. Levchuk, provided that the type of $\Phi$ is different from $C_l$, $l\geqslant 5$ when the characteristic of the ring $K$ is $0$ or $2m$ for some natural number $m>1$. Also, a partial answer to question 19.62 has been obtained.
Keywords: Lie algebra and ring, Chevalley group, commutative ring, carpet of additive subgroups, carpet subgroup. 
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     title = {On the closedness of carpets of additive subgroups associated with a {Chevalley} group over a commutative ring},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Yakov N. Nuzhin. On the closedness of carpets of additive subgroups associated with a Chevalley group over a commutative ring. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 6, pp. 732-737. http://geodesic.mathdoc.fr/item/JSFU_2023_16_6_a2/