A ribbon knot group which has no free base

Author:
Katsuyuki Yoshikawa

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

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the following problem: If a group satisfies the conditions (1) has a finite presentation with generators and relators, and (2) there exists an element of such that where is the normal closure of in , then is 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 -knot group which has no free base.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0934891-7

Keywords:
Knot group,
HNN extension

Article copyright:
© Copyright 1988
American Mathematical Society