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Remarks on a class of 2-generator groups of deficiency zero

Published online by Cambridge University Press:  09 April 2009

C. M. Campbell  and
E. F. Robertson
C. M. Campbell
Affiliation:
Mathematical Institute University of St. AndrewsSt. Andrews, Fife Scotland
E. F. Robertson
Affiliation:
Mathematical Institute University of St. AndrewsSt. Andrews, Fife Scotland
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Let G be a finitely presented group. A finite presentation P of G is said to have defiency m – n if it defines G with m generators and n relations. The deficiency of G is the maximum of the deficiencies of all the finite presentations P of G. If G is finite the deficiency of G is less than or equal to zero. The only finite two generator groups of deficiency zero that are known are certain metacyclic groups given by Wamsley (1970), a class of nilpotent groups given by Macdonald in (1962) and a class of groups given by Wamsley (1972).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 3 , May 1975 , pp. 297 - 305
Copyright
Copyright © Australian Mathematical Society 1975

References

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