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
Full-text PDF Free Access

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
  • P Alfred Pietrowski, The isomorphism problem for one-relator groups with non-trivial centre, Math. Z. 136 (1974), 95–106. MR 0349851
  • KM Goansu Kim and James McCarron, On residually $p$-finite one-relator groups, J. Algebra 169 (1994), 817--826. CMP 95:03

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20E26, 20F05, 20F19

Retrieve articles in all journals with MSC (1991): 20E26, 20F05, 20F19

Additional Information

James McCarron
Affiliation: Department of Pure Mathematics University of Waterloo 200 University Avenue West Waterloo, Ontario Canada N2L 3G1

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