Every group has a terminating transfinite automorphism tower
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- by Joel David Hamkins PDF
- Proc. Amer. Math. Soc. 126 (1998), 3223-3226 Request permission
Abstract:
Iteratively taking the automorphism group of any group leads, transfinitely, to a fixed point.References
- Joel David Hamkins and Simon Thomas, Changing the heights of automorphism towers, submitted to the Annals of Pure and Applied Logic.
- J. A. Hulse, Automorphism towers of polycyclic groups, J. Algebra 16 (1970), 347–398. MR 266986, DOI 10.1016/0021-8693(70)90015-3
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- Simon Thomas, The automorphism tower problem, Proc. Amer. Math. Soc. 95 (1985), no. 2, 166–168. MR 801316, DOI 10.1090/S0002-9939-1985-0801316-9
- Simon Thomas, The automorphism tower problem II, to appear in Israel J. Math.
- H. Wielandt, Eine Verallgemeinerung der invarianten Untergruppen, Math. Z., 45, 1939, 209–244.
Additional Information
- Joel David Hamkins
- Affiliation: Department of Mathematics, City University of New York, College of Staten Island, Staten Island, New York 10314
- MR Author ID: 347679
- Email: hamkins@integral.math.csi.cuny.edu
- 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
- © Copyright 1998 American Mathematical Society
- 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