On Weakly Supplemented Carpets of Lie Type over Commutative Rings

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system’s guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.46698/g1659-3294-1306-k On Weakly Supplemented Carpets of Lie Type over Commutative Rings Badin, P. S. , Nuzhin, Y. N. , Troyanskaya, E. N. Vladikavkaz Mathematical Journal 2021. Vol. 23. Issue 4. Abstract: Relationships between two hypothetical conditions for the closedness of carpets of Lie type over commutative rings are considered. The results of A. K. Gutnova and V. A. Koibaev (Vestnik of Saint Petersburg University, Mathematics. Mechanics. Astronomy, 2020) on the separation of classes of weakly supplemented and supplemented matrix carpets over fields of characteristic 0 and 2 are carried over to carpets of any Lie type over commutative rings even characteristic. It is established that these classes of carpets are also separated by examples of irreducible closed carpets of type \(B_l\) and \(C_l\) over nonperfect fields of characteristic 2, parametrized by two additive subgroups, which were constructed in the work of Ya. N. Nuzhin and A. V. Stepanov (Algebra and Analysis, 2019) to obtain non-standard groups between Chevalley groups over a field and its subfield. Keywords: Chevalley group, carpet of additive subgroups, carpet subgroup, commutative ring Language: Russian Download the full text For citation: Badin, P. S., Nuzhin, Ya. N. and Troyanskaya, E. N. On Weakly Supplemented Carpets of Lie Type over Commutative Rings, Vladikavkaz Math. J., 2021, vol. 23, no. 4, pp.28-34 (in Russian). DOI 10.46698/g1659-3294-1306-k + References 1. Levchuk, V. M. Parabolic Subgroups of Certain ABA-Groups, Mathematical Notes, 1982, vol. 31, no. 4, pp. 259-267. DOI: 10.1007/BF01138934. 2. Nuzhin Ya. N.Lie rings defined by the root system and family of additive subgroups of the initial ring, Proceedings of the Steklov Institute of Mathematics (Supplementary Issues), 2013, vol. 283, suppl. 1, pp. 119-125. DOI: 10.1134/S0081543813090125. 3. The Kourovka notebook: Unsolved Problems in Group Theory, Eds. V. D. Mazurov, E. I. Khukhro, Sobolev Institute of Mathematics, Novosibirsk, 2018, no. 19. 4. Gutnova, A. K. and Koibaev, V. A. On Sufficient Conditions for Closure Elementary Network, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7(65), no. 2, pp. 230-235 (in Russian). DOI: 10.21638/11701. 5. Nuzhin, Ya. N. and Stepanov, A. V. Subgroups of Chevalley Groups of Type \(B_l\) and \(C_l\) Contaning the Group over a Subring, and the Corresponding Carpets, St. Petersburg Mathematical Journal, 2020, vol. 31, no. 4, pp. 719-737. DOI: 10.1090/spmj/1620. ← Contents of issue


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