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

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Ukrainian Mathematical Journal Aims and scope

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. 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 

  3. E. R. Kolchin, “On certain concepts in the theory of algebraic matrix groups,” Ann. Math., 49, 774–789 (1948).

    Article  MathSciNet  Google Scholar 

  4. V. P. Platonov and A. Potapchik, “New combinatorial properties of linear groups,” J. Algebra, 235, No. 1, 399–415 (2001).

    Article  MathSciNet  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).

  6. G. McNinch, “Abelian unipotent subgroups of reductive groups,” J. Pure Appl. Algebra, 167, No. 2-3, 269–300 (2002).

    Article  MathSciNet  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).

  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).

  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).

  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).

  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).

  12. T. Y. Lam, Exercises in Classical Ring Theory, Springer New York (1995).

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Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv, Ukraine

    A. A. Tylyshchak

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  1. A. A. Tylyshchak
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Correspondence to A. A. Tylyshchak.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 8, pp. 1150–1156, August, 2019.

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Tylyshchak, A.A. On Maximal Unipotent Subgroups of a Special Linear Group Over Commutative Ring. Ukr Math J 71, 1312–1319 (2020). https://doi.org/10.1007/s11253-019-01716-6

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  • DOI: https://doi.org/10.1007/s11253-019-01716-6

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