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Limits of covering spaces and residual properties of groups

Published online by Cambridge University Press:  18 May 2009

Jon Michael Corson
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350, USA E-mail: jcorson@ ualvm.ua.edu
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The purpose of this paper is to point out a flaw in H. B. Griffiths' covering space approach to residual properties of groups [3]. One is led to this paper from Lyndon and Schupp's book [4, pp. 114, 141] where it is cited for covering space methods and a proof that F-groups are residually finite. However the main result of [3] is false.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

1.Abels, H., An example of a finitely presented solvable group, Homological group theory, (ed. Wall, C. T. C.), London Mathematical Society Lecture Note Series 36 (Cambridge University Press, 1979), pp. 205211.CrossRefGoogle Scholar
2.Eilenberg, S. and Steenrod, N., Foundations of algebraic topology (Princeton University Press, Princeton, New Jersey, 1952).CrossRefGoogle Scholar
3.Griffiths, H. B., A covering-space approach to residual properties of groups, Michigan Math. J. 14 (1967), 335348.CrossRefGoogle Scholar
4.Lyndon, R. C. and Schupp, P. E., Combinatorial group theory, Ergebnisse der Mathematik, Bd. 89 (Springer, New York, 1977).Google Scholar
5.Magnus, W., Residually finite groups, Bull. Amer. Math. Soc. 75 (1969), 305316.CrossRefGoogle Scholar
6.Magnus, W., Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann. 111 (1935), 259280.CrossRefGoogle Scholar
7.Magnus, W., Karrass, A., and Solitar, D., Combinatorial group theory, 2nd edition (Dover Publications, Inc., New York, 1976).Google Scholar