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Residual finiteness of cyclic extensions of certain free products

Published online by Cambridge University Press:  17 April 2009

Benjamin Baumslag ,
Narain Gupta  and
Frank Levin
Benjamin Baumslag
Affiliation:
Department of Mathematics, Imperial College of Science and Technology, London, England
Narain Gupta
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada
Frank Levin
Affiliation:
Institut für Mathematik, Ruhr-Universität Bochum, Bochum, Federal Republic of Germany
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Abstract

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We prove that a cyclic extension of a free product of finite p-groups is residually finite, p a fixed prime. The question of cyclic extensions of free products of arbitrary cyclic groups remains open.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 2 , October 1978 , pp. 197 - 203
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Baumslag, Benjamin, Tretkoff, Marvin, “Residually finite HNN extensions”, Comm. Algebra 6 (1978), 179–194.CrossRefGoogle Scholar
[2]Baumslag, Gilbert, “Finitely generated cyclic extensions of free groups are residually finite”, Bull. Austral. Math. Soc. 5 (1971), 87–94.CrossRefGoogle Scholar
[3]Magnus, Wilhelm, Karrass, Abraham, Solitar, Donald, 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. Second, revised edition, Dover, New York, 1976).Google Scholar
[4]Mal'cev, A.I., “Generalized nilpotent algebras and their adjoint groups”, Amer. Math. Soc. Transl. (2) 69 (1968), 1–21.Google Scholar