Hostname: page-component-5cf477f64f-zrtmk Total loading time: 0 Render date: 2025-04-04T00:48:30.065Z Has data issue: false hasContentIssue false
  • English
  • Français

On 2-generator 2-relation soluble groups

Published online by Cambridge University Press:  20 January 2009

C. M. Campbell  and
E. F. Robertson
C. M. Campbell
Affiliation:
Mathematical InstituteUniversity of St AndrewsSt Andrews, KY16 9SS
E. F. Robertson
Affiliation:
Mathematical InstituteUniversity of St AndrewsSt Andrews, KY16 9SS
Rights & Permissions [Opens in a new window]

Extract

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.

The class of non-metacyclic finite soluble groups known to have 2-generator 2-relation presentations is small. Classes of such groups are given in (3), (4), (8) and (9). Some subclasses of the groups discussed in (1) and (2) also provide examples, while a class of finite nilpotent 2-generator 2-relation groups is given by Macdonald in (7).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 3 , October 1980 , pp. 269 - 273
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

REFERENCES

(1)Campbell, C. M., Computational techniques and the structure of groups in a certain class, Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation (1976), 312–321.Google Scholar
(2)Campbell, C. M., Coxeter, H. S. M. and Robertson, E. F., Some families of finite groups having two generators and two relations, Proc. Roy. Soc. London A 357 (1977), 423–438.Google Scholar
(3)Campbell, C. M. and Robertson, E. F., Classes of groups related to F a, b, c, Proc. Roy. Soc. Edinburgh 78A (1978), 209–218.Google Scholar
(4)Campbell, C. M. and Robertson, E. F., Deficiency zero groups involving Fibonacci and Lucas numbers, Proc. Roy. Soc. Edinburgh 81A (1978), 273–286.Google Scholar
(5)Johnson, D. L. and Robertson, E. F., Finite groups of deficiency zero, Proc. Durham Sympos, edited by C. T. C. Wall (LMS Lecture Notes, 36 (1979), 275–289).Google Scholar
(6)Johnson, D. L., Wamsley, J. W. and Wright, D., The Fibonacci groups, Proc. London Math. Soc. 29 (1974), 577–592.Google Scholar
(7)MacDonald, I. D., On a class of finitely presented groups, Canad. J. Math. 14 (1962), 602–613.Google Scholar
(8)Wamsley, J. W., A class of two generator two relation finite groups, J. Australian Math. Soc. 14 (1972), 38–40.Google Scholar
(9)Wamsley, J. W., Some finite groups with zero deficiency, J. Australian Math. Soc. 18 (1974), 73–75.Google Scholar