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Proceedings of the American Mathematical Society

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Conjugacy in abelian-by-cyclic groups


Author: James Boler
Journal: Proc. Amer. Math. Soc. 55 (1976), 17-21
DOI: https://doi.org/10.1090/S0002-9939-1976-0399266-2
MathSciNet review: 0399266
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Abstract | References | Additional Information

Abstract: It is shown that each finitely generated torsion-free abelian-by-cyclic group has solvable conjugacy problem. This is done by showing that solving the conjugacy problem for these groups is equivalent to a certain decision problem for modules over the complex group algebra of an infinite cyclic group.


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

  • [1] J. Boler, Embedding and conjugacy in metabelian groups, Thesis, Rice University, 1974.
  • [2] E. Formanek, Matrix techniques in polycyclic groups, Thesis, Rice University, 1970.
  • [3] I. N. Herstein, Topics in algebra, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. MR 0171801
  • [4] W. Magnus, A. Karass and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Pure and Appl. Math., vol. 8, Interscience, New York, 1966, p. 55. MR 34 #7617.


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0399266-2
Keywords: Conjugacy problem, group algebra, group ring
Article copyright: © Copyright 1976 American Mathematical Society