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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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 $H$.


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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