The automorphism tower problem
HTML articles powered by AMS MathViewer
- by Simon Thomas PDF
- Proc. Amer. Math. Soc. 95 (1985), 166-168 Request permission
Abstract:
It is shown that the automorphism tower of an infinite centerless group terminates. For each ordinal $\alpha$, a group is constructed whose automorphism tower terminates in exactly $\alpha$ steps.References
-
E. Fried and J. Kollár Automorphism groups of fields, Universal Algebra (E. T. Schmidt et al., eds.), Colloq. Math. Soc. Janos Boyali, vol. 24, 1981, pp. 293-304.
- J. A. Hulse, Automorphism towers of polycyclic groups, J. Algebra 16 (1970), 347–398. MR 266986, DOI 10.1016/0021-8693(70)90015-3
- Andrew Rae and James E. Roseblade, Automorphism towers of extremal groups, Math. Z. 117 (1970), 70–75. MR 276322, DOI 10.1007/BF01109829
- Derek John Scott Robinson, A course in the theory of groups, Graduate Texts in Mathematics, vol. 80, Springer-Verlag, New York-Berlin, 1982. MR 648604
- Eugene Schenkman, A theory of subinvariant Lie algebras, Amer. J. Math. 73 (1951), 453–474. MR 42399, DOI 10.2307/2372187 O. Schreier and B. L. van der Waerden, Die Automorphismen der projektiven Gruppen, Abh. Math. Sem. Univ. Hamburg 6 (1928), 303-322.
- Helmut Wielandt, Eine Verallgemeinerung der invarianten Untergruppen, Math. Z. 45 (1939), no. 1, 209–244 (German). MR 1545814, DOI 10.1007/BF01580283
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 166-168
- MSC: Primary 20E36
- DOI: https://doi.org/10.1090/S0002-9939-1985-0801316-9
- MathSciNet review: 801316