On Maximal Unipotent Subgroups of a Special Linear Group Over Commutative Ring
- 4 Downloads
It is proved that all maximal unipotent subgroups of a special linear group over commutative ring with identity (such that the factor ring of its modulo primitive radical is a finite direct sum of Bézout domains) are pairwise conjugated and describe one maximal unipotent subgroup of the general linear group (and of a special linear group) over an arbitrary commutative ring with identity.
Unable to display preview. Download preview PDF.
- 1.D. A. Suprunenko, Groups of Matrices [in Russian], Nauka, Moscow (1972).Google Scholar
- 2.A. I. Mal’tsev, “Some classes of infinitely solvable groups,” Mat. Sb., 28, 567–588 (1951).Google Scholar
- 5.O. I. Tavgen’ and S. Yan, “Unipotency of the image of representation of F 2(x, y) in GL(6,C) under the condition of mapping of primitive elements into unipotent matrices,” Vestn. Belorus. Gos. Univ., Ser. 1, No. 2, 114–119 (2010).Google Scholar
- 7.I. I. Simion, “Witt overgroups for unipotent elements in exceptional algebraic groups of bad characteristic,” Mathematica, 57 (80), No. 1-2, 104–116 (2015).Google Scholar
- 8.V. M. Petechuk, “On the triangulation of some unipotent matrix groups over bodies,” Izv. Akad. Nauk Belorus. SSR, Ser. Fiz.-Mat. Nauk, No 6, 44–46 (1987).Google Scholar
- 9.P. M. Gudivok and E. Ya. Pogorilyak, “On the modular representations of finite groups over integral domains,” Tr. Mat. Inst. Akad. Nauk SSSR, 183, 78–86 (1990).Google Scholar
- 10.P. M. Gudivok and V. P. Rud’ko, “On the Sylow subgroups of a general linear group over integral domains,” Dop. Nats. Akad. Nauk Ukr., No. 8, 5–7 (1995).Google Scholar
- 11.A. A. Tylyshchak, “On maximal unipotent subgroups of the general linear group over commutative rings,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauk., No 3, 115–117 (2010).Google Scholar
- 12.T. Y. Lam, Exercises in Classical Ring Theory, Springer New York (1995).Google Scholar