论文标题
$ z $ - 还原群的有限性
Finiteness of $z$-classes in reductive groups
论文作者
论文摘要
让$ k $是一个完美的字段，使得每$ n $都有有限的许多场扩展，直至同构，$ k $ $ n $。如果$ g $是$ k $以上的还原代数组，其特征非常适合$ g $，那么我们证明$ g（k）$只有有限的$ z $ charlasses。 对于每个没有上述有限属性的完美字段$ k $，我们表明存在$ g $以上的$ g $以上，因此$ g（k）$具有无限的许多$ z $ - 类别。
Let $k$ be a perfect field such that for every $n$ there are only finitely many field extensions, up to isomorphism, of $k$ of degree $n$. If $G$ is a reductive algebraic group defined over $k$, whose characteristic is very good for $G$, then we prove that $G(k)$ has only finitely many $z$-classes. For each perfect field $k$ which does not have the above finiteness property we show that there exist groups $G$ over $k$ such that $G(k)$ has infinitely many $z$-classes.
