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On defining groups efficiently without using inverses

Published online by Cambridge University Press:  02 August 2002

C. M. CAMPBELL ,
J. D. MITCHELL  and
N. RUšKUC
C. M. CAMPBELL
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS. e-mail: [email protected]
J. D. MITCHELL
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS. e-mail: [email protected]
N. RUšKUC
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS. e-mail: [email protected]
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Abstract

Let G be a group, and let 〈A[mid ]R〉 be a finite group presentation for G with [mid ]R[mid ][ges ][mid ]A[mid ]. Then there exists a finite semigroup presentation 〈B[mid ]Q〉 for G such that [mid ]Q[mid ]- [mid ]B[mid ] = [mid ]R[mid ]- [mid ]A[mid ]. Moreover, B is either the same generating set or else it contains one additional generator.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 1 , July 2002 , pp. 31 - 36
Copyright
2002 Cambridge Philosophical Society

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