Geodesic
Irreducible carpets of additive subgroups of type $G_2$ over a field of characteristic~$0$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 610-614.

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It is proved that any irreducible carpet of type $G_2$ over a field $F$ of characteristic $0$, at least one additive subgroup of which is an $R$-module, where $F$ is an algebraic extension of the field $R$, up to conjugation by a diagonal element defines a Chevalley group of type $G_2$ over an intermediate subfield between $R$ and $F$.
Keywords: Chevalley group, carpet of additive subgroups, carpet subgroup. 
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Yakov N. Nuzhin; Elizaveta N. Troyanskaya. Irreducible carpets of additive subgroups of type $G_2$ over a field of characteristic~$0$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 610-614. http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a6/

[1] V.M. Levchuk, “Parabolic subgroups of certain ABA-groups”, Mathematical Notes, 31:4 (1982), 509–525 | DOI | MR | Zbl

[2] V. D. Mazurov, E. I. Khukhro (eds.), The Kourovka notebook: Unsolved Problems in Group Theory, 19, Sobolev Institute of Mathematics, Novosibirsk, 2018 | MR

[3] V.M. Levchuk, “On generating sets of root elements of Chevalley groups over a field”, Algebra i Logika, 22:5 (1983), 504–517 (in Russian) | DOI | MR | Zbl

[4] S.K. Franchuk, “On irreducible carpets of additive subgroups of type $G_2$ over fields of characteristic $p>0$”, Vladikavkaz. Matem. J., 22:1 (2020), 78–84 (in Russian) | DOI | MR | Zbl

[5] R. Carter, Simple groups of lie type, Wiley and Sons, London–New York–Sydney–Toronto, 1972 | MR | Zbl

[6] V.A. Koibaev, S.K. Kuklina, A.O. Likhacheva, Ya.N. Nuzhin, “Subgroups, of Chevalley Groups over a Locally Finite Field, Defined by a Family of Additive Subgroups”, Math. Notes, 102:6 (2017), 792–798 | DOI | MR | Zbl