The automorphism tower problem revisited

Winfried Just; Saharon Shelah; Simon Thomas

doi:10.1006/aima.1999.1852

The automorphism tower problem revisited

Winfried Just^*
, Saharon Shelah
, Simon Thomas

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

It is well known that the automorphism towers of infinite centreless groups of cardinality κ terminate in less than (2^κ)⁺ steps. But an easy counting argument shows that (2^κ)⁺ 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.

Original language	English
Pages (from-to)	243-265
Number of pages	23
Journal	Advances in Mathematics
Volume	148
Issue number	2
DOIs	https://doi.org/10.1006/aima.1999.1852
State	Published - 25 Dec 1999

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10.1006/aima.1999.1852

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AB - It is well known that the automorphism towers of infinite centreless groups of cardinality κ terminate in less than (2κ)+ steps. But an easy counting argument shows that (2κ)+ 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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The automorphism tower problem revisited

Abstract

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