Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T01:02:06.861Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  24 October 2008

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

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
Copyright
Copyright © Cambridge Philosophical Society 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Crowell, R. H.. The group G′/G″ of a knot group G. Duke Math. J. 30 (1963), 349354.Google Scholar
[2]Crowell, R. H.. The derived module of a homomorphism. Adv. in Math. 6 (1971), 210222.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), 196210.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. 168176.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), 461472.Google Scholar
[11]Rapaport, E. S.. On the commutator subgroup of a knot group. Ann. of Math. 71 (1960), 157162.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), 415425.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), 571592.Google Scholar
[16]Torres, G. and Fox, R. H.. Dual presentations of the group of a knot. Ann. of Math. 59 (1954), 211218.Google Scholar
[17]Trotter, H. F.. On S-equivalence of Seifert matrices. Inventiones Math. 20 (1973), 173207.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), 655666.CrossRefGoogle Scholar
[19]Trotter, H. F.. Knot modules and Seifert matrices, Knot Theory, Lect. Notes in Math, vol. 685 (Springer Verlag, 1977), 291299.Google Scholar