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The conjugacy problem and cuclic HNN constructions

Published online by Cambridge University Press:  09 April 2009

Leif Larsen
Leif Larsen
Affiliation:
Institute of Math., University of Oslo, Blindern, Oslo 3, Norway
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Abstract

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We consider two related classes of groups. For any group G of the first of these — the smallest class containing all finitely generated free groups and closed under cyclic amalgamations — we show that for any U, W ∈ G we can “effectively describe” the set of all x and y with U* and W* conjugate in G. For the second class, which consists of all groups obtained from the first class through cyclic HNN constructions, we solve the conjugacy and power-conjugacy problems.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 4 , June 1977 , pp. 385 - 401
Copyright
Copyright © Australian Mathematical Society 1977

References

Anshel, Michael and Stebe, Peter (1974), ‘The solvability of the conjugacy problem for certain HNN groups’, Bull. Amer. Math. Soc. 80, 266–270.CrossRefGoogle Scholar
Britton, John L. (1963), ‘The word problem’, Ann. of Math. (2) 77, 16–32.CrossRefGoogle Scholar
Collins, Donald J. (1969), ‘Recursively enumerable degrees and the conjugacy problem’, Ada Math. 122, 115–160.Google Scholar
Larsen, Leif (1976), ‘The solvability of the conjugacy problem for certain free products with amalgamation’, J. Algebra, 43, 28–41.CrossRefGoogle Scholar
Lipschutz, Seymour (1966), ‘Generalization of Dehn's result on the conjugacy problem’, Bull. Amer. Math. Soc. 17, 759–762.Google Scholar
Magnus, Wilhel, Karrass, Abraham, Solitar, Donald (1966), Combinatorial Group Theory: Presentations of groups in terms of generators and relators (Pure and Appl. Math. 13. Interscience [John Wiley & Sons], New York, London, Sydney, 1966).Google Scholar
Miller, Charles F. III, (1971), On Group-Theoretic Decision Problems and Their Classification (Annals of Mathematics Studies, 68. Princeton University Press, University of Tokyo Press, Princeton, New Jersey, 1971).Google Scholar
Miller, Charles F. III, and Schupp, Paul E. (1973), ‘The geometry of Higman-Neuman-Neuman extensions’, Comm. Pure Appl. Math., 26, 787–802.CrossRefGoogle Scholar
Pietrowski, Alfred (1974), ‘The isomorphism problem for one-relator groups with non-trivial centre’, Math. Z. 136, 95–106.CrossRefGoogle Scholar