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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On residually finite knot groups
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by E. J. Mayland PDF
Trans. Amer. Math. Soc. 168 (1972), 221-232 Request permission

Abstract:

The residual finiteness of the class of groups of fibred knots, or those knot groups with finitely generated and, therefore, free commutator subgroups, has been known for some time. Using Baumslag’s results on absolutely parafree groups, this paper extends the result to twist knots (Whitehead doubles of the trivial knot) and certain other classes of nonfibred knots whose minimal spanning surface has complement with free fundamental group. As a by-product more explicit finite representations, namely cyclic extensions of certain $p$-groups, are obtained for these knot groups and the groups of fibred knots. Finally composites of two such knots also have residually finite groups.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 168 (1972), 221-232
  • MSC: Primary 55A25
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0295329-1
  • MathSciNet review: 0295329