Ukrainian Mathematical Journal

, Volume 44, Issue 6, pp 710–718 | Cite as

Commutator structure of some subgroups of chevalley groups

  • V. M. Levchuk


Question 6.34 of the Kourov Notebook is solved: carry the familiar theorem of Merzlyakov on the joint commutator subgroup of covering subgroups over to Chevalley groups and moreover to orthogonal and unitary groups.


Unitary Group Chevalley Group Commutator Subgroup Commutator Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    P. Hall, “A note on SI-groups,” J. London Math. Soc.,39, No. 2, 338–344 (1964).Google Scholar
  2. 2.
    Yu. I. Merzlyakov, “Central series and series of commutator subgroups of matrix groups,” Algebra Logika,3, No. 4, 49–53 (1964).Google Scholar
  3. 3.
    D. A. Suprunenko, “Kernel of a homomorphism,” Sib. Mat. Zh.,6, No. 1, 199–206 (1965).Google Scholar
  4. 4.
    M. I. Kargapolov and Yu. I. Merzlyakov, Foundations of Group Theory [in Russian], Nauka, Moscow (1982).Google Scholar
  5. 5.
    Yu. V. Sosnovskii, “Commutator structure of symplectic groups,” Mat. Zametki,24, No. 5, 641–648 (1978).Google Scholar
  6. 6.
    Yu. V. Sosnovskii, “Orthogonal congruence-subgroups modulo covers of ideals,” in: 14th All-Union Algebra Conference [in Russian], Part 1, Sib. Otd. Inst. Mat., Akad. Nauk SSSR, Novosibirsk (1977), p. 64.Google Scholar
  7. 7.
    H. Roloff, “Lower central series and series of commutator subgroups of net subgroups of the general linear group,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,114, 180–186 (1982).Google Scholar
  8. 8.
    H. Roloff, “Zentralreihen der Netzuntergruppen der Symplektischen Gruppe,” Math. Nachr.,108, No. 2, 241–251 (1982).Google Scholar
  9. 9.
    V. M. Kopytov, V. D. Mazurov, N. S. Romanovskii, et al., Kourov Notebook (Unsolved questions of group theory) [in Russian], 11th edition, Sib. Otd. Inst. Mat., Akad. Nauk SSSR, Novosibirsk (1990).Google Scholar
  10. 10.
    V. M. Levchuk, “A question on Yu. I. Merzlyakov,” in: 8th All-Union Symposium on Group Theory [in Russian], Inst. Mat., Akad. Nauk Ukr. SSR, Kiev (1982), pp. 71–72.Google Scholar
  11. 11.
    V. M. Levchuk, “Central series and series of commutator subgroups of some subgroups of Chevalley groups,” Dokl. Akad. Nauk SSSR,313, No. 4, 799–802 (1990).Google Scholar
  12. 12.
    R. Steinberg, Lectures on Chevalley Groups [Russian translation], Mir, Moscow(1975).Google Scholar
  13. 13.
    V. M. Levchuk, “Parabolic subgroups of some ABA-groups,” Mat. Zametki,31, No. 4, 509–525 (1982).Google Scholar
  14. 14.
    R. Carter, Simple Groups of Lie Type, Wiley and Sons, New York (1972).Google Scholar
  15. 15.
    N. Bourbaki, Lie Groups and Algebras [Russian translation], Mir, Moscow (1982), Chaps. 4–6.Google Scholar
  16. 16.
    E. Abe and K. Suzuki, “On normal subgroups of Chevalley groups over commutative rings,” Tohoku Math. J.,28, No. 2, 185–198 (1976).Google Scholar
  17. 17.
    Yu. E. Vapné, “Central series and commutator subgroup series of some matrix groups,” Sib. Mat. Zh.,12, No. 3, 497–504 (1971).Google Scholar
  18. 18.
    V. I. Yanchevskii, “Lengths of derived series of the group K(2, Z, 2m),” Dokl. Akad. Nauk BSSR,12, No. 12, 1073–1076 (1968).Google Scholar
  19. 19.
    N. A. Vavilov and E. B. Plotkin, “Net subgroups of Chevalley groups. II,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst., Akad. Nauk SSSR,114, 62–76 (1982).Google Scholar
  20. 20.
    E. Abe, “Coverings of twisted Chevalley groups over commutative groups,” Sci. Repts. Tokyo Kyoiku Daigaku,A13, No. 366–382, 194–218 (1977).Google Scholar
  21. 21.
    R. Ree, “On some simple groups defined by C. Chevalley,” Trans. Am. Math. Soc.,84, 392–400 (1957).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • V. M. Levchuk
    • 1
  1. 1.Krasnoyarsk UniversityUSSR

Personalised recommendations