Skip to main content
SpringerLink
Log in

Strongly Lie solvable group algebras of derived length 4

  • Original Paper
  • Published:
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Aims and scope Submit manuscript

Abstract

Let G be a group and let K be a field of characteristic \(p>5\). Necessary and sufficient conditions for the group algebra KG to be strongly Lie solvable of derived length at most 4 have been obtained.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Chandra, H., Sahai, M.: Lie solvable group algebras of derived length three in characteristic three. J. Algebra Appl. 11, 5 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Kulshammer, B., Sharma, R.K.: Lie centrally metabelian group rings in characteristic 3. J. Algebra 180, 111–120 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Levin, F., Rosenberger, G.: Lie metabelian group rings. In: Group and semigroup rings (Johannesburg). North Holland Math Stud., vol. 126. North Holland, Amsterdam, pp. 153–161 (1985)

  • Motose, K., Ninomiya, Y.: On the nilpotency index of the radical of a group algebra. Hokkaido Math. J. 4, 261–264 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  • Passi, I.B.S., Passman, D.S., Sehgal, S.K.: Lie solvable group rings. Can. J. Math. 25(4), 748–757 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  • Rossmanith, R.: Lie centre by metabelian group algebras in even characteristic I. Israel J. Math. 115, 51–75 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • Rossmanith, R.: Lie centre by metabelian group algebras in even characteristic II. Israel J. Math. 115, 77–99 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • Sahai, M.: Group algebras which are Lie solvable of derived length three. J. Algebra Appl. 09(02) (2010)

  • Sahai, M.: Lie solvable group algebras of derived length three. Publ. Math. 39, 233–240 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • Sahai, M.: Group algebras satisfying a certain Lie identity. Commun. Algebra 34(3), 817–828 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Sahai, M., Srivastava, J.B.: A note on Lie centrally metabelian group algebras. J. Algebra 187, 7–15 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Sehgal, S.K.: Topics in Group Rings. Marcel Dekker, New York (1978)

    MATH  Google Scholar 

  • Sharma, R.K., Srivastava, J.B.: Lie solvable rings. Proc. Am. Math. Soc. 94(1), 1–8 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  • Sharma, R.K., Srivastava, J.B.: Lie centrally metabelian group rings. J. Algebra 151(2), 476–486 (1992)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors thank the referee for valuable suggestions that led to a better presentation of the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Delhi, 110016, India

    Reetu Siwach & R. K. Sharma

  2. Department of Mathematics and Astronomy, Lucknow University, Lucknow, 226007, India

    Meena Sahai

Authors
  1. Reetu Siwach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. K. Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Meena Sahai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reetu Siwach.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Siwach, R., Sharma, R.K. & Sahai, M. Strongly Lie solvable group algebras of derived length 4. Beitr Algebra Geom 57, 881–889 (2016). https://doi.org/10.1007/s13366-016-0291-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13366-016-0291-9

Keywords

Mathematics Subject Classification

Search

Navigation