改变自同构塔的高度
Changing the heights of automorphism towers
摘要：
如果$G$是无中心群，则$τ(G)$表示$G$的自同构塔的高度。证明了对每个基数$λ$和序数$α< λ$，存在无中心群$G$使得（a）$τ(G) = α$;（b）如果$β$是任意序数使得$1 \leq β< λ$，则存在强制$P$的概念，它保持共尾性和基数性，使得$τ(G) = β$在相应的类属扩张$V^{P}$中.
英文摘要：
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 $1 \leq β< λ$, then there exists a notion of forcing $P$, which preserves cofinalities and cardinalities, such that $τ(G) = β$ in the corresponding generic extension $V^{P}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
