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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
MathSciNet review:
1487370
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Additional Information
Abstract: Iteratively taking the automorphism group of any group leads, transfinitely, to a fixed point.
- [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, J. Algebra
16 (1970), 347–398. MR 0266986
(42 #1888)
- [1970]
Andrew
Rae and James
E. Roseblade, Automorphism towers of extremal groups, Math. Z.
117 (1970), 70–75. MR 0276322
(43 #2069)
- [1985]
Simon
Thomas, The automorphism tower
problem, Proc. Amer. Math. Soc.
95 (1985), no. 2,
166–168. MR
801316 (86k:20028), http://dx.doi.org/10.1090/S0002-9939-1985-0801316-9
- [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.
- [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:
http://dx.doi.org/10.1090/S0002-9939-98-04797-2
PII:
S 0002-9939(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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