Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-06T10:55:11.969Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Residual Finiteness of Certain Polygonal Products

Published online by Cambridge University Press:  20 November 2018

R. B. J. T. Allenby  and
C. Y. Tang
R. B. J. T. Allenby
Affiliation:
University of Leeds, Leeds, England
C. Y. Tang
Affiliation:
University of Waterloo, Waterloo, Ontario, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give examples to show that unlike generalized free products of groups (g.f.p.) polygonal products of finitely generated (f.g.) nilpotent groups with cyclic amalgamations need not be residually finite (R) and polygonal products of finite p-groups with cyclic amalgamations need not be residually nilpotent. However, polygonal products f.g. abelian groups are R, and under certain conditions polygonal products of finite p-groups with cyclic amalgamations are R.

Keywords

20E0620E2620F1820F05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 11 - 17
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Baumslag, G., on the residual finit eness of generalized free products of nilpotent groups, Trans. Amer. Math. Soc. 106 (1963), pp. 193–209.Google Scholar
2. Brunner, A. M., Frame, M. L., Lee, Y. W. and N. J. Wielenberg, Classifying the torsion-free subgroups of the Picard group, Trans. Amer. Math. Soc. 282 (1984), pp. 205–235.Google Scholar
3. Burns, R. G., A note on free groups, Proc. Amer. Math. Soc. 23 (1969), pp. 14–17. Google Scholar
4. Hall, M., Jr., Coset representations in free groups, Trans. Amer. Math. Soc, 67 (1949), pp. 421–432. Google Scholar
5. Higman, G., Amalgam of p-groups, J. of Algebra 1 (1964), pp. 301–305. Google Scholar
6. Karrass, A., Pietrowski, A. and Solitar, D., The subgroups of polygonal products of groups, unpublished manuscript.Google Scholar
7. Neumann, B. H., An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. London, Ser. A 246 (1954), pp. 503–554.Google Scholar
8. Neumann, B. H. and H. Neumann, A contribution to the embedding theory of group amalgams, Proc. London Math. Soc. (3) 3 (1953), pp. 243–256. Google Scholar
9. Wiegold, J., Nilpotent products of groups with amalgamations, Publ. Math. Debrecen 6 (1959), pp. 131–168. Google Scholar