In 1905 I. Shur pointed out the largest dimension of commutative subgroups in the groups SL(n, C) and proved that for n > 3 such the subgroups are automorphic to each other. In 1945 A.I. Mal’tsev investigated the problem of description of the largest dimension commutative subgroups in the simple complex Lie groups. He solved the problem by the transition to the complex Lie algebras and by the reduction to the same problem for the maximal nilpotent subalgebra. Let N be a niltriangular subalgebra of a Chevalley algebra. The article deals with the problem of describing the largest dimension commutative subalgebras of N over an arbitrary field. The solution of this problem is obtained for the subalgebra N of E₆ type Chevalley algebra.

Evgeniya Kirillova, Postgraduate Student, Siberian Federal University, 79 Svobodny pr., Krasnoyarsk, 660041, Russian Federation, tel.: (391)2062148, e-mail: kea92@bk.ru

Kirillova E.A. Generalized Reduced Mal’tsev Problem on Commutative Subalgebras of E₆ Type Chevalley Algebras over a Field. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 29, pp. 31-38. https://doi.org/10.26516/1997-7670.2019.29.31

1. Barry M.J.J. Large Abelian subgroups of Chevalley groups. J. Austral. Math. Soc. Ser. A., 1979, vol. 27, no. 1, pp. 59-87. https://doi.org/10.1017/S1446788700016645
2. Carter R. Simple groups of Lie type. Wiley and Sons, New York, 1972, 331 p.
3. Kirillova E.A., Suleimanova G.S. Highest dimension commutative ideals of a niltriangular subalgebra of a Chevalley algebra over a field. Trudy Inst. Mat. i Mekh. UrO RAN, 2018, vol. 24, no. 3, pp. 98-108. (in Russian) https://doi.org/10.21538/0134-4889-2018-24-3-98-108
4. Kondrat’ev A.S. Subgroups of finite Chevalley groups. Uspekhi Mat. Nauk, 1986, vol. 41, no. 1 (247), pp. 57-96. (in Russian) https://doi.org/10.1070/RM1986v041n01ABEH003203
5. Levchuk V.M., Suleimanova G.S. Extremal and maximal normal abelian subgroups of a maximal unipotent subgroup in groups of Lie type. J. Algebra, 2012, vol. 349, iss. 1, no. 1, pp. 98-116.
6. Levchuk V.M., Suleimanova G.S. The generalized Mal’cev problem on abelian subalgebras of the Chevalley algebras. Lobachevskii Journal of Mathematics, 2015, vol. 86, no. 4, pp. 384-388.
7. Levchuk V.M., Suleimanova G.S. Thompson subgroups and large abelian unipotent subgroups of Lie-type groups. J. Siberian Federal University. Math. & Physics, 2013, vol. 6, no. 1, pp. 64-74.
8. Malcev A.I. Commutative subalgebras of semi-simple Lie algebras. Izv. Akad. Nauk SSSR Ser. Mat., 1945, vol. 9, no. 4, pp. 291–300. (in Russian)
9. Schur I. Zur theorie der vertauschbaren matrizen. J. reine und angew. Math., 1905, vol. 130, pp. 66-76. https://doi.org/10.1515/crll.1905.130.66
10. Vdovin E.P. Large abelian unipotent subgroups of finite Chevalley groups. Algebra and Logic, 2001, vol. 40, no. 5, pp. 292-305. (in Russian) https://doi.org/10.1023/A:1012549701336
11. Vdovin E.P. Maximal Orders of Abelian Subgroups in Finite Chevalley Groups. Mat. Zametki, 2001, vol. 69, no. 4, pp. 524-549. (in Russian)