论文标题
整个扭转，独特的根特性和Baumslag-结式的关系
Generalized torsion, unique root property and Baumslag--Solitar relation for knot groups
论文作者
论文摘要
让$ g $成为一个小组。如果等式$ x^n = y^n $ in $ g $表示任何元素$ x $和$ y $的$ x = y $，则$ g $称为$ r $ - 组。完全理解哪些结组为$ r $ - 组。 Fay和Walls引入了$ \ bar {r} $ - 组，其中$ \ langle x \ rangle $ comincide的归一化器和中央器对于任何非平凡的元素$ x $ comingide。众所周知，$ \ bar {r} $ - 组和$ r $ - 组共享许多有趣的属性，$ \ bar {r} $ - 组必然是$ r $ - 组。但是，总的来说，匡威不存在。我们将证明这些课程对于结组是相同的。在证明过程中，我们将确定带有阶命令二的扭转的结组。
Let $G$ be a group. If an equation $x^n = y^n$ in $G$ implies $x = y$ for any elements $x$ and $y$, then $G$ is called an $R$--group. It is completely understood which knot groups are $R$--groups. Fay and Walls introduced $\bar{R}$--group in which the normalizer and the centralizer of an isolator of $\langle x \rangle$ coincide for any non-trivial element $x$. It is known that $\bar{R}$--groups and $R$--groups share many interesting properties and $\bar{R}$--groups are necessarily $R$--groups. However, in general, the converse does not hold. We will prove that these classes are the same for knot groups. In the course of the proof, we will determine knot groups with generalized torsion of order two.
