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Finitely generated subgroups and the centre of some factor groups of free products

Published online by Cambridge University Press:  17 April 2009

C.K. Gupta  and
N. Romanovski
C.K. Gupta
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada, e-mail: [email protected]
N. Romanovski
Affiliation:
Institute of Mathematics, Novosibirsk 63009, Russia, e-mail: [email protected]
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For groups of the type F/[R, R], where F is a free product, we prove a generalisation of a theorem of Karrass and Solitar on a finitely generated subgroup of a free product containing a nontrivial subnormal subgroup. We also describe the centre of the group F[/R, R].

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 239 - 244
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Karrass, A. and Solitar, D., ‘On finitely generated subgroups of a free product’, Math. Z. 108 (1969), 285–287.CrossRefGoogle Scholar
[2]Auslander, M. and Lyndon, R.C., ‘Commutator subgroups of free groups’, Amer. J. Math. 77 (1955), 929–931.CrossRefGoogle Scholar
[3]Romanovski, N., ‘On Shmel'kin embeddings for abstract and profinite groups’, Algebra and Logic 38 (1999), 482–494.CrossRefGoogle Scholar