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The automorphism tower problem revisited

Winfried Just·Saharon Shelah·Simon Thomas
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Abstract

It is well-known that the automorphism towers of infinite centreless groups of cardinality kappa terminate in less than (2^{kappa})^+ steps. But an easy counting argument shows that (2^{kappa})^+ is not the best possible bound. However, in this paper, we will show that it is impossible to find an explicit better bound using ZFC.

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Winfried Just, Saharon Shelah, Simon Thomas. 2000-03-20. The automorphism tower problem revisited. https://arxiv.org/abs/math/0003120

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