Mathematical Proceedings of the Cambridge Philosophical Society



On defining groups efficiently without using inverses


C. M. CAMPBELL a1, J. D. MITCHELL a2 and N. RUŠKUC a3
a1 Mathematical Institute, University of St Andrews, St Andrews KY16 9SS. e-mail: cmc@st-and.ac.uk
a2 Mathematical Institute, University of St Andrews, St Andrews KY16 9SS. e-mail: jamesm@mcs.st-and.ac.uk
a3 Mathematical Institute, University of St Andrews, St Andrews KY16 9SS. e-mail: nik@mcs.st-and.ac.uk

Abstract

Let G be a group, and let [left angle bracket]A[mid R:]R[right angle bracket] be a finite group presentation for G with [mid R:]R[mid R:][gt-or-equal, slanted][mid R:]A[mid R:]. Then there exists a finite semigroup presentation [left angle bracket]B[mid R:]Q[right angle bracket] for G such that [mid R:]Q[mid R:]- [mid R:]B[mid R:] = [mid R:]R[mid R:]- [mid R:]A[mid R:]. Moreover, B is either the same generating set or else it contains one additional generator.

(Received November 14 2000)
(Revised December 11 2000)