Generalized Torsion in Knot Groups

作者：Naylor Geoff^*; Rolfsen Dale^*

来源：Canadian Mathematical Bulletin, 2016, 59(1): 182-189.

DOI：10.4153/CMB-2015-004-4

• knot group
• generalized torsion
• ordered group

In a group, a nonidentity element is called a generalized torsion element if some product of its conjugates equals the identity. We show that for many classical knots one can find generalized torsion in the fundamental group of its complement, commonly called the knot group. It follows that such a group is not bi-orderable. Examples include all torus knots, the (hyperbolic) knot 5(2), and algebraic knots in the sense of Milnor.

• 出版日期2016-3