This article is cited in 1 paper

On weakly supplemented carpets of Lie type over commutative rings

P. S. Badin, Ya. N. Nuzhin, E. N. Troyanskaya

Institute of Mathematics and Computer Science, Siberian Federal University, 79 Svobodny Ave., Krasnoyarsk 660041, Russia

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.

Key words: Chevalley group, carpet of additive subgroups, carpet subgroup, commutative ring.

UDC: 512.552.1

MSC: 20G15

Received: 06.07.2021

DOI: 10.46698/g1659-3294-1306-k