标题： 分次除法代数的Whitehead群的扭子群 显示英文标题

标题： Torsion subgroups of Whitehead groups of graded division algebras

摘要： 在本文中，我们研究了分次除法代数 $E$ 的 Whitehead 群 $E^*/[E^*,E^*]$ 的挠子群，该挠子群记为 ${\rm TK}_1(E)$。特别是，我们在一些特殊情况下提供了 ${\rm TK}_1(E)$ 的公式，例如当 $E$ 未分支、完全分支或半分支时。利用这些公式，我们可以计算一个赋值除法环 $D$ 的群 ${\rm TK}_1(D)$，该除法环在其 henselian 中心上是有限维的。 显示英文摘要

摘要： In this paper, we study the torsion subgroup, which is denoted by ${\rm TK}_1(E)$, of the Whitehead group $E^*/[E^*,E^*]$ of a graded division algebra $E$ which is finite dimensional over its center. In particular, we provide formulas for ${\rm TK}_1(E)$ in some special cases such as when $E$ is unramified, totally ramified or semiramified. Using the formulas, we are able to compute the group ${\rm TK}_1(D)$ of a valued division ring $D$, which is finite dimensional over a henselian center.