Skip to main content
SpringerLink
Log in

On finite bases for laws of triangular matrices

  • Surveys
  • Conference paper
  • First Online:
Groups—Canberra 1989

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1456))

  • 546 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hanna Neumann, Varieties of groups, Ergebnisse der Mathematik und ihrer Grenzgebiete 37 (Springer-Verlag, Berlin, 1967).

    Google Scholar 

  2. Ju.A. Bahturin, Lectures on Lie algebras, Studien zur Algebra und ihrer Anwendungen 4 (Akademie-Verlag, Berlin, 1978).

    Google Scholar 

  3. B.I. Plotkin, ‘Varieties of group representations’, Usp. Mat. Nauk. 32 (1977), 3–68 (in Russian). English translation: Russian Math. Surveys 32 (1977) no. 5, 1–72.

    MathSciNet  MATH  Google Scholar 

  4. Ju.P. Razmyslov, ‘Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero’, Algebria i Logika 12 (1973), 83–113 (in Russian). English translation: Algebra and Logic 12 (1973), 47–63 (1974).

    MathSciNet  Google Scholar 

  5. B.H. Neumann, ‘Identical relations in groups, I’, Math. Ann. 114 (1937), 506–525.

    Article  MathSciNet  MATH  Google Scholar 

  6. A.Ju. Ol’shankskii, ‘On the problem of a finite basis of identities in groups’, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 376–384 (in Russian). English translation: Math. USSR—Izv. 4 (1970), 381–389 (1971).

    MathSciNet  Google Scholar 

  7. S.I. Adyan, ‘Infinite irreducible systems of group identities’, Dokl. Akad. Nauk SSSR 190 (1970), 499–501 (in Russian). English translation: Soviet Math. Dokl. 11 (1970), 113–115.

    MathSciNet  MATH  Google Scholar 

  8. M.R. Vaughan-Lee, ‘Uncountably many varieties of groups’, Bull. London Math. Soc. 2 (1970), 280–286.

    Article  MathSciNet  MATH  Google Scholar 

  9. V.P. Platonov, ‘Linear groups with identical relations’, Dokl. Akad. Nauk SSSR 11 (1967), 581–582 (in Russian).

    MathSciNet  Google Scholar 

  10. D.E. Cohen, ‘On the laws of a metabelian variety’, J. Algebra 5 (1967), 267–273.

    Article  MathSciNet  MATH  Google Scholar 

  11. John Cossey, ‘Laws in nilpotent-by-finite groups’, Proc. Amer. Math. Soc 19 (1968), 685–688.

    Article  MathSciNet  MATH  Google Scholar 

  12. A.N. Krasil’nikov, ‘On the finiteness of bases of laws of nilpotent-by-abelian groups’ (in Russian, to appear).

    Google Scholar 

  13. R.M. Bryant and M.F. Newman, ‘Some finitely based varieties of groups’, J. London Math. Soc. (3) 28 (1974), 237–252.

    Article  MathSciNet  MATH  Google Scholar 

  14. A.N. Krasil’nikov and A.L. Shmel’kin, ‘On the Specht property and basis rank of some products of varieties of groups’, Algebra i Logika 20 (1981), 546–554 (in Russian). English translation: Algebra and Logic 20 (1981), 357–363 (1982).

    MathSciNet  Google Scholar 

  15. S.M. Vovsi and Nguen Khung Shon, ‘Identities of almost stable representations of groups’, Mat. Sb. 132 (174) (1987), 578–591 (in Russian). English translation: Math. USSR—Sb. 60 (1988), 569–581.

    Google Scholar 

  16. A.N. Krasil’nikov, ‘On the laws of triangular matrix representations of groups’, Trudy Moskovsk. Mat. Obshch. 52 (1989), 229–245 (in Russian).

    MATH  Google Scholar 

  17. A.N. Krasil’nikov and A.L. Shmel’kin, ‘On the laws of finite dimensional representations of solvable Lie algebras and groups’, in Algebra—Some current trends, ed. by L. L. Avramov and K. B. Tchakerian, Lecture Notes in Math. 1352, pp. 114–129 (Springer-Verlag, Berlin, 1988).

    Chapter  Google Scholar 

  18. A.N. Krasil’nikov, ‘The finite basis property for certain varieties of Lie algebras’, Vestnik Moskov. Univ. Ser. I. Mat. Mekh. (1982), no. 2, 34–38 (in Russian). English translation: Moscow Univ. Math. Bull. 37 (1982), no. 2, 44–48.

    Google Scholar 

  19. Ju.A. Bahturin and A.Ju. Ol’shanskii, ‘Identical relations in finite Lie rings’, Mat. Sb. 96 (1975), 543–559 (in Russian).

    MathSciNet  MATH  Google Scholar 

  20. M.R. Vaughan-Lee, ‘Varieties of Lie algebras’, Quart. J. Math. Oxford Ser. (2) 21 (1970), 297–308.

    Article  MathSciNet  MATH  Google Scholar 

  21. V.S. Drenski, ‘On identities in Lie algebras’, Algebra i Logika 13 (1974), 265–290 (in Russian). English translation: Algebra and Logic 13 (1974), 150–165 (1975).

    Article  MathSciNet  Google Scholar 

  22. A.N. Krasil’nikov, ‘On the laws of nilpotent-by-abelian Lie algebras over a field of finite characteristic’ (in Russian, to appear).

    Google Scholar 

  23. R.M. Bryant and M.R. Vaughan-Lee, ‘Soluble varieties of Lie algebras’, Quart. J. Math. Oxford Ser. (2) 23 (1972), 107–112.

    Article  MathSciNet  MATH  Google Scholar 

  24. A.N. Krasil’nikov, ‘On the finiteness of bases of laws of finite dimensional representations of solvable Lie algebras, II’ (in Russian, to appear).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Moscow Pedagogical Institute, Krasnoprudnaya ul. 14, 107140, Moscow, USSR

    A. N. Krasil’nikov

  2. Department of Mathematics and Mechanics, Moscow State University, Leninskie Gory, 119899, Moscow, USSR

    A. L. Shmel’kin

Authors
  1. A. N. Krasil’nikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. L. Shmel’kin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

L. G. Kovács

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Krasil’nikov, A.N., Shmel’kin, A.L. (1990). On finite bases for laws of triangular matrices. In: Kovács, L.G. (eds) Groups—Canberra 1989. Lecture Notes in Mathematics, vol 1456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100727

Download citation

  • DOI: https://doi.org/10.1007/BFb0100727

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53475-4

  • Online ISBN: 978-3-540-46900-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation