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Finitely Generated Subgroups of HNN Groups

Published online by Cambridge University Press:  20 November 2018

R. G. Burns
R. G. Burns*
Affiliation:
York University, Downsview, Ontario
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In this paper we give sufficient conditions for an HNN group to have the following two properties:

(1) any two finitely generated subgroups intersect in a finitely generated subgroup;

(2) every finitely generated subgroup containing a non-trivial subnormal subgroup has finite index.

The following result is a particular case of the main theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 1103 - 1112
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Burns, R. G., On the finitely generated subgroups of an amalgamated product of two groups Trans. Amer. Math. Soc. 169 (1972), 293–306.Google Scholar
2. Cohen, D. E., Subgroups of HNN groups (to appear).Google Scholar
3. Karrass, A. and Solitar, D., Subgroups of HNN groups and groups with one defining relation, Can. J. Math. 23 (1971), 627–643.Google Scholar
4. Moldavanskii, D. I., The intersection of finitely generated subgroups, Sibirsk.Mat.Ž. 9 (1968), 1422–1426.Google Scholar
5. Oxley, P. C., Ends of groups and a related construction, Ph.D. Thesis, Queen Mary College, 1971.Google Scholar