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Hermitian character and the first problem of R. H. Fox

Published online by Cambridge University Press:  24 October 2008

Adrian Pizer
Adrian Pizer
Affiliation:
Department of Mathematics, Osaka City University, Japan
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Extract

Let G be a group such that

(1) G is finitely presented with deficiency one,

(2) G/G' is infinite cyclic, with a distinguished generator t.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 3 , November 1985 , pp. 447 - 458
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Crowell, R. H.. The group G′/G″ of a knot group G. Duke Math. J. 30 (1963), 349–354.Google Scholar
[2]Crowell, R. H.. The derived module of a homomorphism. Adv. in Math. 6 (1971), 210–222.Google Scholar
[3]Crowell, R. H. and Fox, R. H.. Introduction to Knot Theory (Ginn Blaisdell, 1963).Google Scholar
[4]Fox, R. H.. Free differential calculus 2. Ann. of Math. 59 (1954), 196–210.CrossRefGoogle Scholar
[5]Fox, R. H.. Some problems in knot theory. Topology of 3-Manifolds and Related Topics, ed. Fort, M. K. Jr. (Prentice-Hall, 1962), pp. 168–176.Google Scholar
[6]Lang, S.. Algebra (Addison-Wesley World Student Series Edition, 2nd printing, 1970).Google Scholar
[7]Newman, M.. Integral Matrices, Pure and Applied Mathematics Series, vol. 45 (Academic Press, 1972).Google Scholar
[8]Noethcott, D. G.. An Introduction to Homological Algebra (Cambridge University Press, reprint, 1st ed., 1962).Google Scholar
[9]O'Meara, O. T.. Introduction to Quadratic Forms, Grundlehren der Math. Wissenschaften 117 (Springer-Verlag, 1963).CrossRefGoogle Scholar
[10]Pizer, A.. Matrices over group rings which are Alexander matrices. Osaka J. Math. 21 (1984), 461–472.Google Scholar
[11]Rapaport, E. S.. On the commutator subgroup of a knot group. Ann. of Math. 71 (1960), 157–162.Google Scholar
[12]Rolfsen, D.. Knots and Links (Publish or Perish, 1976).Google Scholar
[13]Rolfsen, D.. A surgical view of Alexander's polynomial, Geometric Topology, ed. Glaser, L. C. and Rushing, T. B.. Lect. Notes in Math., vol. 438 (Springer-Verlag, 1975), 415–425.Google Scholar
[14]Schreier, O. and Sperner, E.. Modern Algebra and Matrix Theory (New York, 1951).Google Scholar
[15]Seifert, H.. Über das Geschlect von Knoten. Math. Ann 110 (1934), 571–592.Google Scholar
[16]Torres, G. and Fox, R. H.. Dual presentations of the group of a knot. Ann. of Math. 59 (1954), 211–218.Google Scholar
[17]Trotter, H. F.. On S-equivalence of Seifert matrices. Inventiones Math. 20 (1973), 173–207.CrossRefGoogle Scholar
[18]Trotter, H. F.. Torsion free metabelian groups with infinite cyclic quotient groups. Proc. Second Internal. Conf. Theory of Groups, Lect. Notes in Math. vol.372 (Springer-Verlag, 1973), 655–666.CrossRefGoogle Scholar
[19]Trotter, H. F.. Knot modules and Seifert matrices, Knot Theory, Lect. Notes in Math, vol. 685 (Springer Verlag, 1977), 291–299.Google Scholar