Conjugate powers in HNN groups

Anshel, Michael

doi:10.1090/S0002-9939-1976-0393249-4

Conjugate powers in HNN groups

Author: Michael Anshel
Journal: Proc. Amer. Math. Soc. 54 (1976), 19-23
DOI: https://doi.org/10.1090/S0002-9939-1976-0393249-4
MathSciNet review: 0393249
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Abstract | References | Additional Information

Abstract: Our purpose is to show the conjugacy problem is solvable for certain groups with many stable letters and in the process investigate conjugate powers in these groups.

[1] Michael Anshel, Non-Hopfian groups with fully invariant kernels. II, J. Algebra 24 (1973), 473–485. MR 0313406, https://doi.org/10.1016/0021-8693(73)90121-X
[2] Michael Anshel and Peter Stebe, The solvability of the conjugacy problem for certain HNN groups, Bull. Amer. Math. Soc. 80 (1974), 266–270. MR 0419615, https://doi.org/10.1090/S0002-9904-1974-13455-5
[3] Benjamin Baumslag, Generalized free products whose two-generator subgroups are free, J. London Math. Soc. 43 (1968), 601–606. MR 0233896, https://doi.org/10.1112/jlms/s1-43.1.601
[4a] Gilbert Baumslag, On generalised free products, Math. Z. 78 (1962), 423–438. MR 0140562, https://doi.org/10.1007/BF01195185
[4b] -, Lecture notes in nilpotent groups, CBMS Regional Conf. Ser. in Math., no. 2, Amer. Math. Soc., Providence, R.I., 1971. MR 44 #315.
[5] C. R. J. Clapham, The conjugacy problem for a free product with amalgamation, Arch. Math. (Basel) 22 (1971), 358–362. MR 0306338, https://doi.org/10.1007/BF01222587
[6] A. Karrass and D. Solitar, The free product of two groups with a malnormal amalgamated subgroup, Canad. J. Math. 23 (1971), 933–959. MR 0314992, https://doi.org/10.4153/CJM-1971-102-8
[7] A. G. Kurosh, The theory of groups, Chelsea Publishing Co., New York, 1960. Translated from the Russian and edited by K. A. Hirsch. 2nd English ed. 2 volumes. MR 0109842
[8] Seymour Lipschutz, Generalization of Dehn’s result on the conjugacy problem, Proc. Amer. math. Soc. 17 (1966), 759–762. MR 0197541, https://doi.org/10.1090/S0002-9939-1966-0197541-1
[9] Wilhelm Magnus, Noneuclidean tesselations and their groups, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Pure and Applied Mathematics, Vol. 61. MR 0352287
[10] Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1966. MR 0207802
[11] Charles F. Miller III, On group-theoretic decision problems and their classification, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. Annals of Mathematics Studies, No. 68. MR 0310044

Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0393249-4
Keywords: groups with many stable letters, conjugate powers, conjugacy and generalized conjugacy problem, word and generalized word problem, -group, residually-free and -free, malnormal, reachability problem
Article copyright: © Copyright 1976 American Mathematical Society