Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A ribbon knot group which has no free base
HTML articles powered by AMS MathViewer

by Katsuyuki Yoshikawa PDF
Proc. Amer. Math. Soc. 102 (1988), 1065-1070 Request permission

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57Q45, 20E06, 20F05
  • Retrieve articles in all journals with MSC: 57Q45, 20E06, 20F05
Additional 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