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A note on groups with separable finitely generated subgroups

Published online by Cambridge University Press:  17 April 2009

R. G. Burns ,
A. Karrass  and
D. Solitar
R. G. Burns
Affiliation:
Department of Mathematics, York University, North York, Ontario, M3J 1P3Canada.
A. Karrass
Affiliation:
Department of Mathematics, York University, North York, Ontario, M3J 1P3Canada.
D. Solitar
Affiliation:
Department of Mathematics, York University, North York, Ontario, M3J 1P3Canada.
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Abstract

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An example is given of an infinite cyclic extension of a free group of finite rank in which not every finitely generated subgroup is finitely separable. This answers negatively the question of Peter Scott as to whether in all finitely generated 3-manifold groups the finitely generated subgroups are finitely separable. In the positive direction it is shown that in knot groups and one-relator groups with centre, the finitely generated normal subgroups are finitely separable.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 1 , August 1987 , pp. 153 - 160
Copyright
Copyright © Australian Mathematical Society 1987

References

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