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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 $ HNN$ groups with many stable letters and in the process investigate conjugate powers in these groups.

References [Enhancements On Off] (What's this?)

  • [1] M. Anshel, Non-Hopfian groups with fully invariant kernels. II, J. Algebra 24 (1973), 473-485. MR 47 #1960. MR 0313406 (47:1960)
  • [2] M. Anshel and P. Stebe, The solvability of the conjugacy problem for certain $ HNN$ groups, Bull. Amer. Math. Soc. 80 (1974), 266-270. MR 0419615 (54:7633)
  • [3] B. Baumslag, Generalized free products whose two-generator subgroups are free, J. London Math. Soc. 43 (1968), 601-606. MR 38 #2217. MR 0233896 (38:2217)
  • [4a] G. Baumslag, On generalised free products, Math. Z. 78 (1962), 423-438. MR 25 #3980. MR 0140562 (25:3980)
  • [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 46 #5464. MR 0306338 (46:5464)
  • [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 47 #3541. MR 0314992 (47:3541)
  • [7] A. G. Kuroš, Theory of groups, 2nd ed., GITTL, Moscow, 1953; English transl., Vol. II, Chelsea, New York, 1960. MR 15, 501; 22 #727. MR 0109842 (22:727)
  • [8] S. Lipschutz, Generalization of Dehn's result on the conjugacy problem, Proc. Amer. Math. Soc. 17 (1966), 759-762. MR 33 #5706. MR 0197541 (33:5706)
  • [9] W. Magnus, Noneuclidean tesselations and their groups, Academic Press, New York and London, 1974. MR 0352287 (50:4774)
  • [10] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory: Presentation of groups in terms of generators and relations, Pure and Appl. Math., vol. 13, Interscience, New York, 1966. MR 34 #7617. MR 0207802 (34:7617)
  • [11] C. F. Miller III, On group-theoretic decision problems and their classification, Ann. of Math. Studies, no. 68, Princeton Univ. Press, Princeton, N.J.; Univ. of Tokyo Press, Tokyo, 1971. MR 46 #9147. MR 0310044 (46:9147)

Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0393249-4
Keywords: $ HNN$ groups with many stable letters, conjugate powers, conjugacy and generalized conjugacy problem, word and generalized word problem, $ U$-group, residually-free and $ 2$-free, malnormal, reachability problem
Article copyright: © Copyright 1976 American Mathematical Society

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