Skip to main content
Log in

TheS 3-conjecture for solvable groups

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

This paper solves theS 3-conjecture for solvable groups proving that a nontrivial finite solvable group in which no two distinct conjugacy classes have the same order is isomorphic toS 3.

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

  • [AT] J.H. Conway, R. Curtis, S. Norton, R. Parker and R. Wilson,Atlas of Finite Groups, Clarendon Press, Oxford, 1985.

    MATH  Google Scholar 

  • [BCH] Y. Berkovich, D. Chillag and M. Herzog,Finite groups in which the degrees of the nonlinear irreducible characters are distinct, Proceedings of the American Mathematical Society115 (1992), 955–959.

    Article  MATH  MathSciNet  Google Scholar 

  • [BMH] M. Bianchi, A. Mauri and M. Herzog,Groups with non-central classes of distinct lengths, preprint, 1990.

  • [FS] W. Feit and G.M. Seitz,On finite rational groups and related topics, Illinois Nournal of Mathematics33 (1989), 103–131.

    MATH  MathSciNet  Google Scholar 

  • [Gi] A.L. Gilotti,Sui gruppi finiti in cui classi distinte de elementi coniugate hanno diversa cardinalita, Atti Accad. Naz. Linceî Rend.58 (1975), 501–507.

    MATH  MathSciNet  Google Scholar 

  • [Go] R. Gow,Groups whose characters are rational-valued, Journal of Algebra40 (1976), 280–299.

    Article  MATH  MathSciNet  Google Scholar 

  • [Gs] D. Gorenstein,Finite Groups, Harper and Row, New York, 1968.

    MATH  Google Scholar 

  • [Ha] M. Hayashi,On a generalization of F.M. Markel's theorem, Hokkaido Mathematical Journal4 (1975), 278–280.

    MATH  MathSciNet  Google Scholar 

  • [Hu] B. Huppert,Endliche Gruppen I, Springer-Verlag, Berlin, 1983.

    Google Scholar 

  • [Is] M. Isaacs,Character Theory of Finite Groups, Academic Press, New York, 1976.

    MATH  Google Scholar 

  • [Ma] A. Mann,On groups with conjugacy classes of distinct sizes, unpublished.

  • [Mk] F.M. Markel,Groups with many conjugate elements, Journal of Algebra26 (1973), 69–74.

    Article  MATH  MathSciNet  Google Scholar 

  • [Wa] M.B. Ward,Finite groups in which no two distinct conjugacy classes have the same order, Archiv der Mathematik54 (1990), 111–116.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Knörr, R., Lempken, W. & Thielcke, B. TheS 3-conjecture for solvable groups. Israel J. Math. 91, 61–76 (1995). https://doi.org/10.1007/BF02761639

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02761639

Keywords

Navigation