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Every group has a terminating transfinite automorphism tower


Author: Joel David Hamkins
Journal: Proc. Amer. Math. Soc. 126 (1998), 3223-3226
MSC (1991): Primary 20E36, 20F28
DOI: https://doi.org/10.1090/S0002-9939-98-04797-2
MathSciNet review: 1487370
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Abstract: Iteratively taking the automorphism group of any group leads, transfinitely, to a fixed point.


References [Enhancements On Off] (What's this?)

  • [1997] Joel David Hamkins and Simon Thomas, Changing the heights of automorphism towers, submitted to the Annals of Pure and Applied Logic.
  • [1970] J. A. Hulse, Automorphism towers of polycyclic groups, Journal of Algebra, 16, 1970, 347-398. MR 42:1888
  • [1970] Andrew Rae and James E. Roseblade, Automorphism Towers of Extremal Groups, Math. Z., 70-75, 1970, 117. MR 43:2069
  • [1985] Simon Thomas, The automorphism tower problem, Proceedings of the American Mathematical Society, 95, 1985, 166-168. MR 86k:20028
  • [1998] Simon Thomas, The automorphism tower problem II, to appear in Israel J. Math.
  • [1939] H. Wielandt, Eine Verallgemeinerung der invarianten Untergruppen, Math. Z., 45, 1939, 209-244.

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Additional Information

Joel David Hamkins
Affiliation: Department of Mathematics, City University of New York, College of Staten Island, Staten Island, New York 10314
Email: hamkins@integral.math.csi.cuny.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04797-2
Received by editor(s): April 9, 1997
Additional Notes: The author’s research has been supported in part by a grant from the PSC-CUNY Research Foundation. He would like to thank both Daniel Seabold and Daniel Velleman for pointing out a simplification in the proof.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society

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