Skip to main content
Log in

Integral Group Rings With All Central Units Trivial: Solvable Groups

  • Published:
Indian Journal of Pure and Applied Mathematics Aims and scope Submit manuscript

Abstract

The object of this paper is to examine finite solvable groups whose integral group rings have only trivial central units.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. R. Arora and I. B. S. Passi, Central height of the unit group of an integral group ring, Comm. Algebra, 21(10) (1993), 3673–3683.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. K. Bakshi, S. Maheshwary, and I. B. S. Passi, Integral group rings with all central units trivial, J. Pure Appl. Algebra, 221(8) (2017), 1955–1965.

    Article  MathSciNet  MATH  Google Scholar 

  3. D. Chillag and S. Dolfi, Semi-rational solvable groups, J. Group Theory, 13(4) (2010), 535–548.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Dokuchaev, C. P. Milies and S. K. Sehgal, Integral group rings with trivial central units. II, Comm. Algebra, 33(1) (2005), 37–42.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. W. Golomb and A. W. Hales, On enumerative equivalence of group elements, J. Combinatorial Theory, 5 (1968), 308–312.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Gow, Schur indices of some groups of Lie type, J. Algebra, 42(1) (1976), 102–120.

    Article  MathSciNet  MATH  Google Scholar 

  7. G. Higman, The units of group-rings, Proc. London Math. Soc. (2), 46 (1940), 231–248.

    Article  MathSciNet  MATH  Google Scholar 

  8. G. Higman, Finite groups in which every element has prime-power order, J. London Math. Soc., 32 (1957), 335–342.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Ritter and S. K. Sehgal, Integral group rings with trivial central units, Proc. Amer. Math. Soc., 108(2) (1990), 327–329.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sugandha Maheshwary.

Additional information

Research supported by DST-SERB, India (PDF/2016/000731).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maheshwary, S. Integral Group Rings With All Central Units Trivial: Solvable Groups. Indian J Pure Appl Math 49, 169–175 (2018). https://doi.org/10.1007/s13226-018-0260-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13226-018-0260-0

Key words

Navigation