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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
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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

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