论文标题
$κ$ - 已关闭集团的自态
Automorphisms of $κ$-existentially closed groups
论文作者
论文摘要
我们研究了一些$κ$ - 存在的封闭组的自动形态。特别是，我们证明$ aut（g）$是保存自动形态的亚组和$ | aut（g）| = 2^κ$的结合，只要$κ$不可访问，$ g $是独特的$κ$ - $κ$ - 具有封闭的封闭性的Cardinatity $κ$。的确，后一个结果是一个论点的副产品表明，对于任何不可数的$κ$和任何$ g $的$ g $，这是定期表示长度$κ$的限制，我们具有$ | aut（g）| = \ beth_ {κ{κ+1} $，而$ \ beth $是$ \ beth $。如果$κ$是常规的，此类群体也已关闭$κ$。这两个结果均通过对此类组的自动形态的分析和分类来获得。
We investigate the automorphisms of some $κ$- existentially closed groups. In particular, we prove that $Aut(G)$ is the union of subgroups of level preserving automorphisms and $|Aut(G)|=2^κ$ whenever $κ$ is inaccessible and $G$ is the unique $κ$-existentially closed group of cardinality $κ$. Indeed, the latter result is a byproduct of an argument showing that, for any uncountable $κ$ and any group $G$ that is the limit of regular representation of length $κ$ with countable base, we have $|Aut(G)|=\beth_{κ+1}$, where $\beth$ is the beth function. Such groups are also $κ$-existentially closed if $κ$ is regular. Both results are obtained by an analysis and classification of level preserving automorphisms of such groups.
