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Subgroups of HNN groups

Published online by Cambridge University Press:  09 April 2009

D. E. Cohen
D. E. Cohen
Affiliation:
Queen Mary College, University of London, Mile End Road, London EI, 4NS, England
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The purpose of this paper is to give a more precise form of Theorem 1 of [2], which gives a structure theorem for subgroups of HNN groups; we prove the following.

Let H be a subgroup of the HNN group <A, xi;xiU-ixi-1 = Ui>. Then H is an HNN group whose base is a tree product of groups H ∪ wAw-1 where w runs over a set of double coset representatives of (H,A); the amalgamated and associated subgroups are all of the form H ∊ vUiv-l for some v. We can be more precise about which subgroups occur and about the tree product. We will also obtain stronger forms of other results in [1] and [2].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 4 , June 1974 , pp. 394 - 405
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Karrass, A. and Solitar, D., ‘The subgroups of a free product of two groups with an amalgamated subgroups’, Trans. Amer. Math, Soc. 149 (1970), 227–255.CrossRefGoogle Scholar
[2]Karrass, A. and Soliar, D., ‘Subgroups of HNN groups and groups with one defining relations’, Canadian J. Math. 23 (1971), 627–543.CrossRefGoogle Scholar
[3]Oxley, P. C., Ends of groups and a related construction, (Ph. D. Thesis, Queen Mary College, 1972.)Google Scholar
[4]Serre, J. -P., Groupes discretes, (Springer Lecture Notes (to appear).)Google Scholar