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Finitely generated subgroups of amalgamated free products and HNN groups

Published online by Cambridge University Press:  09 April 2009

Daniel E. Cohen
Daniel E. Cohen
Affiliation:
Department of Pure Mathematics, Queen Mary College, London University, England.
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Abstract

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The theory of groups acting on trees due to Bass and Serre (1969) is applied to simplify some results of Burns (1972, 1973) giving conditions under which an amalgamated free product or HNN extension has the properties that any finitely generated subgroup containing an infinite subnormal subgroup must have finite index and that the intersection of two finitely generated subgroups is finitely generated.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 3 , November 1976 , pp. 274 - 281
Copyright
Copyright © Australian Mathematical Society 1976

References

Burns, R. G. (1972), ‘On the finitely generated subgroups of an amalgamated product of two groups’, Trans Amer. Math. Soc. 169, 293–306.CrossRefGoogle Scholar
Burns, R. G. (1973), ‘Finitely generated subgroups of HNN groups’, Canad. J. Math. 25, 1103–1112.Google Scholar
Cohen, D. E. (1974), ‘Subgroups of HNN groups’, J. Austral. Math. Soc. 17, 394–405.CrossRefGoogle Scholar
Moldavanskiiˇ, D. I. (1968), ‘The intersection of finitely generated subgroups’, (Russian), Sibirsk. Mat. Z`. 9, 1422–1426Google Scholar
(English translation in Siberian Math. J. 9, 1066–1069 (1969)).Google Scholar
Serre, J.-P. (1969), Groupes Discretes (Lecture Notes, Collège de France).Google Scholar