Abstract
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core, and Alexander quandles) is established. Further, residual finiteness of automorphism groups of some residually finite quandles is also discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 3621-3633 |
| Number of pages | 13 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 147 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Aug 2019 |
Keywords
- 3-manifold group
- Enveloping group
- Free quandle
- Knot group
- Knot quandle
- Peripheral subgroup
- Residually finite quandle
- enveloping group
- knot quandle
- peripheral subgroup
- free quandle
- knot group
- residually finite quandle
OECD FOS+WOS
- 1.01 MATHEMATICS