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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Residually nilpotent one-relator groups
with nontrivial centre


Author: James McCarron
Journal: Proc. Amer. Math. Soc. 124 (1996), 1-5
MSC (1991): Primary 20E26, 20F05, 20F19
MathSciNet review: 1301037
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Abstract | References | Similar Articles | Additional Information

Abstract: We determine explicitly the residually nilpotent one-relator groups with nontrivial centre. We show also that, if $G$ is a one-relator group, then $G$ is residually nilpotent if, and only if, its central quotient $G/Z(G)$ is residually nilpotent.


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

  • M James McCarron, Residual nilpotence and one relator groups, Ph.D. Thesis, University of Waterloo, 1995, in preparation.
  • G K. W. Gruenberg, Residual properties of infinite soluble groups, Proc. London Math. Soc. (3) 7 (1957), 29–62. MR 0087652 (19,386a)
  • P Alfred Pietrowski, The isomorphism problem for one-relator groups with non-trivial centre, Math. Z. 136 (1974), 95–106. MR 0349851 (50 #2344)
  • KM Goansu Kim and James McCarron, On residually $p$-finite one-relator groups, J. Algebra 169 (1994), 817--826. CMP 95:03

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Additional Information

James McCarron
Affiliation: Department of Pure Mathematics \ University of Waterloo \ 200 University Avenue West \ Waterloo, Ontario \ Canada N2L 3G1
Email: jmccarron@jeeves.uwaterloo.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03148-6
PII: S 0002-9939(96)03148-6
Keywords: Residually nilpotent, residually $p$-finite, one-relator group, compact
Received by editor(s): May 5, 1994
Additional Notes: The contents of this note form a part of the author’s Ph.D. thesis. It is a pleasure to thank my supervisor, F. C. Y. Tang, for his help and guidance
Communicated by: Ronald Solomon
Article copyright: © Copyright 1996 American Mathematical Society