Israel Journal of Mathematics

, Volume 103, Issue 1, pp 93–109 | Cite as

The automorphism tower problem II

  • Simon ThomasEmail author


We prove that the automorphism tower of every infinite centreless groupG of cardinality κ terminates in less than (2κ)+ steps. We also show that it is consistent withZFC that the automorphism tower of every infinite centreless groupG of regular cardinality κ actually terminates in less than 2κ steps.


Outer Automorphism Regular Cardinal Follow Diagram Commute Conservative Extension Canonical Embedding 
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  1. [1]
    J. E. Baumgartner,Iterated forcing, inSurveys in Set Theory (A.R.D. Mathias, ed.), Cambridge University Press, 1983, pp. 1–59.Google Scholar
  2. [2]
    M. Foreman and H. Woodin,GCH can fail everywhere, Annals of Mathematics133 (1991), 1–35.CrossRefMathSciNetGoogle Scholar
  3. [3]
    E. Fried and J. Kollár,Automorphism groups of fields, inUniversal Algebra (E. T. Schmidt et al., eds.), Coloq. Math. Soc. Janos Boyali, Vol. 24, 1981, pp. 293–304.Google Scholar
  4. [4]
    J. A. Hulse,Automorphism towers of polycyclic groups, Journal of Algebra16 (1970), 347–398.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    T. Jech,Set Theory, Academic Press, New York, 1978.Google Scholar
  6. [6]
    A. Kanamori and M. Magidor,The evolution of large cardinal axioms in set theory, inHigher Set Theory (G. H. Müller and D. S. Scott, eds.), Lecture Notes in Mathematics699, Springer, Berlin, 1978, pp. 99–275.CrossRefGoogle Scholar
  7. [7]
    H. D. Macpherson and P. M. Neumann,Subgroups of infinite symmetric groups, Journal of the London Mathematical Society (2)42 (1990), 64–84.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    T. K. Menas,Consistency results concerning supercompactness, Transactions of the American Mathematical Society223 (1976), 61–91.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    W. R. Scott,Group Theory, Prentice-Hall, New Jersey, 1964.zbMATHGoogle Scholar
  10. [10]
    S. Thomas,The automorphism tower problem, Proceedings of the American Mathematical Society95 (1985), 166–168.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    H. Wielandt,Eine Verallgemeinerung der invarianten Untergruppen, Mathematische Zeitschrift45 (1939), 209–244.CrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1998

Authors and Affiliations

  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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