标题： 八交叉以下的纽结拟群的双向性 显示英文标题

标题： Biorderability of knot quandles of knots up to eight crossings

摘要： 本文研究了前八交叉点的素纽结的纽结拟群的双序性。我们证明了纽结拟群$6_3$，$8_7$，$8_8$，$8_{10}$和$8_{16}$不能是双可排序的。 然而，我们看到 Knot Quandles of Knots $4_1$, $6_1$, $6_2$, $7_6$, $7_7$, $8_1$, $8_2$, $8_3$, $8_4$, $8_5$, $8_6$, $8_9$, $8_{11}$, $8_{12}$, $8_{13}$, $8_{14}$, $8_{17}$, $8_{18}$, $8_{20}$和 $8_{21}$可能是双序化的。 我们还给出了这些纽结的纽结拟群生成集上的线性序，其中这些纽结中的某些纽结的拟群上这种线性序可以扩展为拟群上的双序。 显示英文摘要

摘要： The paper investigates biorderability of knot quandles of prime knots up to eight crossings. We prove that knot quandles of knots $6_3$, $8_7$, $8_8$, $8_{10}$ and $8_{16}$ can not be biorderable. However, we see that knot quandles of knots $4_1$, $6_1$, $6_2$, $7_6$, $7_7$, $8_1$, $8_2$, $8_3$, $8_4$, $8_5$, $8_6$, $8_9$, $8_{11}$, $8_{12}$, $8_{13}$, $8_{14}$, $8_{17}$, $8_{18}$, $8_{20}$ and $8_{21}$ could be biorderable. We also give linear orders on the generating set of the knot quandle of a knot (among these knots) that could be extendable to biorders on the quandle.