Homogeneity and complete decomposability of torsion free knot modules

Katsuyuki YOSHIKAWA

doi:10.2969/jmsj/04310101

Katsuyuki YOSHIKAWA

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 1 Pages 101-116

DOI https://doi.org/10.2969/jmsj/04310101

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Published: 1991 Received: June 15, 1989 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. Baer, Abelian groups without elements of finite order, Duke Math. J., 3 (1937), 68-122.
2) R. H. Crowell, The group G'/G” of a knot group G, Duke Math. J., 30 (1963), 349-354.
3) L. Fuchs, Infinite Abelian Groups, vol. 1, 2, Pure Appl. Math., 36, Academic Press, 1970.
4) J. C. Hausmann and M. Kervaire, Sous-groupes dérivés des groupes de noeuds, Enseign. Math., 24 (1978), 111-123.
5) M. Kervaire. Les noeuds de dimensions supérieures, Bull. Soc. Math. France, 93 (1965), 225-271.
6) J. Levine, Some results on higher dimensional knot groups, Lecture Notes in Math., 685, Springer, 1978, 243-273.
7) J. Levine, Algebraic Structure of Knot Modules, Lecture Notes in Math., 772, Springer, 1980.
8) E. S. Rapaport, On the commutator subgroup of a knot group, Ann. Math., 71 (1960), 157-162.
9) D. W. Sumners, Polynomial invariants and the integral homology of coverings of knots and links, Invent. Math., 15 (1972), 78-90.

Right : [1] R. Baer, Abelian groups without elements of finite order, Duke Math. J., 3 (1937), 68-122.
[2] R. H. Crowell, The group G'/G" of a knot group G, Duke Math. J., 30 (1963), 349-354.
[3] L. Fuchs, Infinite Abelian Groups, vol. 1, 2, Pure Appl. Math., 36, Academic Press, 1970.
[4] J. C. Hausmann and M. Kervaire, Sous-groupes dérivés des groupes de noeuds, Enseign. Math., 24 (1978), 111-123.
[5] M. Kervaire. Les noeuds de dimensions supérieures, Bull. Soc. Math. France, 93 (1965), 225-271.
[6] J. Levine, Some results on higher dimensional knot groups, Lecture Notes in Math., 685, Springer, 1978, 243-273.
[7] J. Levine, Algebraic Structure of Knot Modules, Lecture Notes in Math., 772, Springer, 1980.
[8] E. S. Rapaport, On the commutator subgroup of a knot group, Ann. Math., 71 (1960), 157-162.
[9] D. W. Sumners, Polynomial invariants and the integral homology of coverings of knots and links, Invent. Math., 15 (1972), 78-90.

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