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.
KeywordsOuter Automorphism Regular Cardinal Follow Diagram Commute Conservative Extension Canonical Embedding
Unable to display preview. Download preview PDF.
- J. E. Baumgartner,Iterated forcing, inSurveys in Set Theory (A.R.D. Mathias, ed.), Cambridge University Press, 1983, pp. 1–59.Google Scholar
- 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
- T. Jech,Set Theory, Academic Press, New York, 1978.Google Scholar