Proceedings of the Edinburgh Mathematical Society (Series 2)
- Proceedings of the Edinburgh Mathematical Society (Series 2) / Volume 19 / Issue 01 / March 1974, pp 25-29
- Copyright © Edinburgh Mathematical Society 1974
- DOI: http://dx.doi.org/10.1017/S0013091500015315 (About DOI), Published online: 20 January 2009
Research Article
A class of finite groups with zero deficiency
J. W. Wamsleya1
a1 The Flinders University of South Australia
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.
(Received December 08 1972)
- (1 ) Macdonald, I. D., On a class of finitely presented groups, Canad. J. Math. 14 (1962), 602–613. [OpenURL Query Data] [Google Scholar]
- (2 ) Wamsley, J. W., Minimal presentations for certain group extensions, Israel J. Math. 9 (1971), 459–463. [OpenURL Query Data] [CrossRef] [Google Scholar]
- (3 ) Wamsley, J. W., A class of three-generator, three-relation, finite groups, Canad. J. Math. 22 (1970), 36–50. [OpenURL Query Data] [Google Scholar]
