Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T01:14:18.194Z Has data issue: false hasContentIssue false
  • English
  • Français

A class of finite groups with zero deficiency

Published online by Cambridge University Press:  20 January 2009

J. W. Wamsley
J. W. Wamsley
Affiliation:
The Flinders University of South Australia
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.

Let G be a finite group generated by n elements and defined by m relations, then G has a presentation, G = {x1, …, xn | R1, …, Rm} = F/R where F is free on generators x1, …, xn and R is the normal closure in F of R1, …, Rm. The deficiency of this presentation is n − m. Since G is finite the deficiency is non-positive and the deficiency of G is the maximal over the deficiencies of all presentations for G.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 1 , March 1974 , pp. 25 - 29
Copyright
Copyright © Edinburgh Mathematical Society 1974

References

REFERENCES

(1) Macdonald, I. D., On a class of finitely presented groups, Canad. J. Math. 14 (1962), 602–613.CrossRefGoogle Scholar
(2) Wamsley, J. W., Minimal presentations for certain group extensions, Israel J. Math. 9 (1971), 459–463.CrossRefGoogle Scholar
(3) Wamsley, J. W., A class of three-generator, three-relation, finite groups, Canad. J. Math. 22 (1970), 36–50.CrossRefGoogle Scholar