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Ukrainian Mathematical Journal

, Volume 71, Issue 8, pp 1312–1319 | Cite as

On Maximal Unipotent Subgroups of a Special Linear Group Over Commutative Ring

  • A. A. TylyshchakEmail author
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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.

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References

  1. 1.
    D. A. Suprunenko, Groups of Matrices [in Russian], Nauka, Moscow (1972).Google Scholar
  2. 2.
    A. I. Mal’tsev, “Some classes of infinitely solvable groups,” Mat. Sb., 28, 567–588 (1951).Google Scholar
  3. 3.
    E. R. Kolchin, “On certain concepts in the theory of algebraic matrix groups,” Ann. Math., 49, 774–789 (1948).MathSciNetCrossRefGoogle Scholar
  4. 4.
    V. P. Platonov and A. Potapchik, “New combinatorial properties of linear groups,” J. Algebra, 235, No. 1, 399–415 (2001).MathSciNetCrossRefGoogle Scholar
  5. 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
  6. 6.
    G. McNinch, “Abelian unipotent subgroups of reductive groups,” J. Pure Appl. Algebra, 167, No. 2-3, 269–300 (2002).MathSciNetCrossRefGoogle Scholar
  7. 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. 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. 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. 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. 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. 12.
    T. Y. Lam, Exercises in Classical Ring Theory, Springer New York (1995).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Shevchenko Kyiv National UniversityKyivUkraine

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