论文标题
Chevalley组的有界生成和换向器宽度：功能案例
Bounded generation and commutator width of Chevalley groups: function case
论文作者
论文摘要
我们证明，多项式戒指上的Chevalley小组$ \ Mathbb f_q [t] $以及laurent polyenmial $ \ mathbb f_q [t，t^{ - 1}] $ rings，其中$ \ mathbb f_q $是有限的领域，是一个有限的领域。使用此，我们产生了这些组的换向器宽度的明确界限。在一些其他假设下，我们证明了其他类别的雪佛兰群体在积极特征中的算术环上的反射环。作为推论，我们对有限田定义的仿期kac- moody组的换向器宽度产生明确的估计。该论文还包含了有关谎言类型组，某些应用程序和该领域未解决问题列表的有限生成问题的更广泛讨论。
We prove that Chevalley groups over polynomial rings $\mathbb F_q[t]$ and over Laurent polynomial $\mathbb F_q[t,t^{-1}]$ rings, where $\mathbb F_q$ is a finite field, are boundedly elementarily generated. Using this we produce explicit bounds of the commutator width of these groups. Under some additional assumptions, we prove similar results for other classes of Chevalley groups over Dedekind rings of arithmetic rings in positive characteristic. As a corollary, we produce explicit estimates for the commutator width of affine Kac--Moody groups defined over finite fields. The paper contains also a broader discussion of the bounded generation problem for groups of Lie type, some applications and a list of unsolved problems in the field.
