## A ribbon knot group which has no free base

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- by Katsuyuki Yoshikawa
- Proc. Amer. Math. Soc.
**102**(1988), 1065-1070 - DOI: https://doi.org/10.1090/S0002-9939-1988-0934891-7
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## Abstract:

We consider the following problem: If a group $G$ satisfies the conditions (1) $G$ has a finite presentation with $r + 1$ generators and $r$ relators, and (2) there exists an element $x$ of $G$ such that $G = {\left \langle {\left \langle x \right \rangle } \right \rangle ^G}$ where ${\left \langle {\left \langle x \right \rangle } \right \rangle ^G}$ is the normal closure of $x$ in $G$, then is $G$ an HNN (Higman-Neumann-Neumann) extension of a free group of finite rank? In this paper, we give a negative answer to the problem. Thus it follows that there exists a ribbon $n$-knot group $(n \geq 2)$ which has no free base.## References

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## Bibliographic Information

- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**102**(1988), 1065-1070 - MSC: Primary 57Q45; Secondary 20E06, 20F05
- DOI: https://doi.org/10.1090/S0002-9939-1988-0934891-7
- MathSciNet review: 934891