Abstract
If G is a centreless group, then τ(G) denotes the height of the automorphism tower of G. We prove that it is consistent that for every cardinal λ and every ordinal α<λ, there exists a centreless group G such that (a) τ(G)=α; and (b) if β is any ordinal such that 1⩽β<λ, then there exists a notion of forcing P , which preserves cofinalities and cardinalities, such that τ(G)=β in the corresponding generic extension V P .
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