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Transactions of the American Mathematical Society

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On residually finite knot groups


Author: E. J. Mayland
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1972-0295329-1
Article copyright: © Copyright 1972 American Mathematical Society

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