Geodesic
Extraction of small rank unipotent elements in $\mathrm{GL}(4,K)$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 134-148 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present paper we prove that in the group $\mathrm{GL}(4,K)$ over the field which has at least 19 elements the subgroup generated by a pair of 2-tori contains unipotent elements of rank 1 or 2. Keeping in mind the papers of N.A. Vavilov and author this result is valid for any general linear group. This paper is one of the first step of studying of the subgroups generated by a pair of microweight tori in Chevalley groups. 
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     title = {Extraction of small rank unipotent elements in $\mathrm{GL}(4,K)$},
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V. V. Nesterov. Extraction of small rank unipotent elements in $\mathrm{GL}(4,K)$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 134-148. http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a9/

[1] Z. I. Borevich, “Opisanie podgrupp polnoi lineinoi gruppy, soderzhaschikh gruppu diagonalnykh matrits”, Zap. nauchn. semin. LOMI, 64, 1976, 12–29 | Zbl

[2] N. A. Vavilov, “Podgruppy grupp Shevalle, soderzhaschie maksimalnyi tor”, Trudy Leningr. Mat. Obschestva, 1 (1990), 64–109

[3] N. A. Vavilov, “Geometriya $1$-torov v $\mathrm{GL}_n$”, Algebra i Analiz, 19:3 (2007), 120–151

[4] N. A. Vavilov, V. V. Nesterov, “Geometriya mikrovesovykh torov”, Vladikavkazskii mat. zhurnal, 10:1 (2008), 10–23 | MR | Zbl

[5] V. V.Nesterov, N. A. Vavilov, Pairs of microweight tori in $\mathrm{GL}_n$, 2020, 11 pp.

[6] N. A. Vavilov, V. V. Nesterov, Podgruppy, porozhdennye paroi 2-torov v $\mathrm{GL}_5(K)$, predlozheno v pechat

[7] R. Lidl, G. Niderraiter, Konechnye polya, v. 1, Mir, M., 1988, 430 pp. | MR

[8] H. Azad, “Root groups”, J. Algebra, 76:1 (1982), 211–213 | DOI | MR | Zbl

[9] A. M. Cohen, H. Cuypers, H. Sterk, “Linear groups generated by reflection tori”, Canad. J. Math., 51:6 (1999), 1149–1174 | DOI | MR | Zbl

[10] E. Cline, B. Parshall, L. Scott, “Minimal elements of $N(H,P)$ and conjugacy of Levi complements in finite Chevalley groups”, J. Algebra, 34:3 (1975), 521–523 | DOI | MR | Zbl

[11] A. J. Hahn, O. T. O'Meara, The classical groups and K-theory, Springer, Berlin et al., 1989 | MR | Zbl

[12] G. Seitz, “Small rank permutation representations of finite Chevalley groups”, J. Algebra, 28:3 (1974), 508–517 | DOI | MR | Zbl