论文标题
二维Artin组的山雀替代方案和Wise的权力替代方案
The Tits Alternative for two-dimensional Artin groups and Wise's Power Alternative
论文作者
论文摘要
我们表明，二维Artin团体可以满足山雀替代方案的加强：它们的子组包含一个非亚洲自由群体，或者实际上是$ 2 $的自由级别的Abelian。 When in addition the associated Coxeter group is hyperbolic, we answer in the affirmative a question of Wise on the subgroups generated by large powers of two elements: given any two elements $a, b$ of a two-dimensional Artin group of hyperbolic type, there exists an integer $n\geq 1$ such that $a^n$ and $b^n$ either commute or generate a non-abelian free subgroup.
We show that two-dimensional Artin groups satisfy a strengthening of the Tits alternative: their subgroups either contain a non-abelian free group or are virtually free abelian of rank at most $2$. When in addition the associated Coxeter group is hyperbolic, we answer in the affirmative a question of Wise on the subgroups generated by large powers of two elements: given any two elements $a, b$ of a two-dimensional Artin group of hyperbolic type, there exists an integer $n\geq 1$ such that $a^n$ and $b^n$ either commute or generate a non-abelian free subgroup.
