Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T09:42:48.204Z Has data issue: false hasContentIssue false
  • English
  • Français

Some results on symmetrically-presented groups

Published online by Cambridge University Press:  20 January 2009

D. L. Johnson  and
R. W. K. Odoni
D. L. Johnson
Affiliation:
Mathematics DepartmentUniversity of NottinghamUniversity Park Nottingham NG7 2RD
R. W. K. Odoni
Affiliation:
Mathematics DepartmentUniversity of GlasgowUniversity Gardens Glasgow G12 8QW
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.

Necessary and sufficient conditions are found on an ideal a⊲ℤ[x] for the additive group [a]+ of ℤ[x]/a to be finite and cyclic. As a consequence, the abelianizations of certain cyclically-presented groups are computed explicitly.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 2 , June 1994 , pp. 227 - 237
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

1.Bunder, M. W., Johnson, D. L. and Kim, A.-C., The exponents of Fibonacci algebras, Fibonacci Quarterly, submitted.Google Scholar
2.Campbell, C. M. and Robertson, E. F., The orders of certain metacyclic groups, Bull. London Math. Soc. 6 (1974), 312–314.CrossRefGoogle Scholar
3.Conway, J. H., Advanced problem 5327, Amer. Math. Monthly 72 (1965), 915.Google Scholar
4.Conway, J. H., Solution to advanced problem 5327, Amer. Math Monthly 74 (1967), 91–93.CrossRefGoogle Scholar
5.Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras John Wiley, New York 1962).Google Scholar
6.Johnson, D. L., A note on the Fibonacci groups, Israel J. Math. 17 (1974), 27–282.CrossRefGoogle Scholar
7.Johnson, D. L. and Kim, A.-C., Cyclic Fibonacci algebras, in preparation.Google Scholar
8.Thomas, R. M., The Fibonacci groups revisited, in Groups St Andrews 1989 (eds. Campbell, C. M. and Robertson, E. F.), CUP, Cambridge 1991, 445–454.CrossRefGoogle Scholar
9.Thomas, R. M., On a question of Kim concerning certain group presentations, Bull. Korean Math. Soc. 28 (1991), 219–224.Google Scholar