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Generalized torsion, unique root property and Baumslag--Solitar relation for knot groups | | Keisuke Himeno
; Kimihiko Motegi
; Masakazu Teragaito
; | | Date: |
1 Aug 2022 | | Abstract: | 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
$ar{R}$--group in which the normalizer and the centralizer of an isolator of
$langle x
angle$ coincide for any non-trivial element $x$. It is known that
$ar{R}$--groups and $R$--groups share many interesting properties and
$ar{R}$--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. | | Source: | arXiv, 2208.00621 | | Services: | Forum | Review | PDF | Favorites | |
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