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Infinite cyclic verbal subgroups
of relatively free groups


Author: A. Storozhev
Journal: Proc. Amer. Math. Soc. 124 (1996), 2953-2954
MSC (1991): Primary 20E10, 20F06
DOI: https://doi.org/10.1090/S0002-9939-96-03521-6
MathSciNet review: 1343726
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Abstract: We prove that there exist a relatively free group $H$ and a word $w(x,y)$ in two variables such that the verbal subgroup of $H$ defined by $w(x,y)$ is an infinite cyclic group whereas $w(x,y)$ has only one nontrivial value in $H$.


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

  • [1] S.V. Ivanov, P. Hall's conjecture on the finiteness of verbal subgroups, Izv. Vyssh. Ucheb. Zaved. 325 (1989), 60--70. MR 90j:20061
  • [2] Kourovka Notebook, Unsolved problems of the group theory, Tenth Edition, Novosibirsk, 1986.
  • [3] Kourovka Notebook, Unsolved problems of the group theory, Eleventh Edition, Novosibirsk, 1991.
  • [4] A.Yu. Ol'shanskii, Geometry of defining relations in groups, Mathematics and Its Applications (Soviet Series), vol. 70, Kluwer Academic Publishers, Dordrecht, 1991. MR 93g:20071
  • [5] A. Storozhev, On abelian subgroups of relatively free groups, Comm. Algebra 22 (1994), 2677--2701. MR 95d:20066
  • [6] R.F. Turner-Smith, Marginal subgroup properties for outer commutator words, Proc. London. Math. Soc. 14 (1964), 321--341. MR 29:2289

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Additional Information

A. Storozhev
Affiliation: Australian Mathematics Trust, University of Canberra, PO Box 1, Belconnen, ACT 2616, Australia
Email: ans@amt.canberra.edu.au

DOI: https://doi.org/10.1090/S0002-9939-96-03521-6
Received by editor(s): March 6, 1995
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1996 American Mathematical Society

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