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Subgroups with centre in HNN groups

Published online by Cambridge University Press:  09 April 2009

D. Solitar
Affiliation:
Department of Mathematics, York University, Downsview, Ontario M3J 1PS, Canada.
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Abstract

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A subgroup with non-trivial centre in a one-relator group is shown to be a treed HNN group (graph product) with infinite cyclic vertices. Moreover, subgroups with non-trivial centre in HNN groups are also examined.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

Bagherzadeh, G. H. (1976), ‘Commutativity in one-relator groups’, J. London Math. Soc. (2) 13. 459471.CrossRefGoogle Scholar
Bieri, R. (to appear). ‘Duality groups and groups of cohomological dimension two that are extensions’.Google Scholar
Cohen, Daniel E. (1973), ‘Groups with the free subgroups of finite index’, Conference on Group Theory. University of Wisconsin-Parkside 1972 (Lecture Notes in Mathematics. 319, 2644Springer-Verlag. Berlin, Heidelberg, New York, 1973).CrossRefGoogle Scholar
Cossey, John and Smythe, N. (1975), ‘HNN groups and groups with center’, Knots, Groups, and 3-manifolds (Annals of Mathematics Studies, 84, 8799. Princeton University Press and University of Tokyo Press, Princeton, New Jersey, 1975).CrossRefGoogle Scholar
Epstein, D. B. A. (1962), ‘A result on free products with amalgamation’, J. London Math. Soc. 37, 130132.CrossRefGoogle Scholar
Karrass, A., Pietrowski, A. and Solitar, D. (1974), ‘An improved subgroup theorem for HNN groups with some applications’, Canad. J. Math. 26, 214224.CrossRefGoogle Scholar
Karrass, A. and Solitar, D. (1970). ‘The subgroups of a free product of two groups with and amalgamated subgroup’, Trans. Amer. Math. Soc. 150, 227255.CrossRefGoogle Scholar
Karrass, A. and Solitar, D. (1971). ‘Subgroups of HNN groups and groups with one defining relation’, Canad. J. Math. 23, 627643.CrossRefGoogle Scholar
Magnus, Wilhelm, Karrass, Abraham, Solitar, Donald (1966), Combinatorial Group Theory: Presentations of groups in terms of generators and relations (Pure and Appl. Math. 13. Interscience [John Wiley & Sons], New York, London, Sydney, 1966).Google Scholar
Молдаванский, л. и [D. I. Moldavanskiì] (1967), ‘O некоторьих полгруппах групп с оДн им определяющлп сооТнощни’ [Certain subgroups of groups with one defining relation’], Sibirsk. Mat. Z`. 8, 13701384.Google ScholarPubMed
Scott, G. P. (1974), ‘An embedding theorem for groups with a free subgroup of finite index’, Bull. London Math. Soc. 6, 304306.CrossRefGoogle Scholar