Abstract
A finite group defined by n generators and m relations must have m ⩾ n. A finite group is said to have deficiency zero if it has a presentation with n generators and n relations. In 1907 Schur [13] proved important results showing that certain finite groups could not have deficiency zero presentations. Let SL(2, p) denote the group of 2 X 2 matrices of determinant 1 over the field GF(p) p an odd prime, and put PSL(2, p) = SL(2, p)/{±I}. Now PSL(2, p) and SL(2,p) can be generated by two elements, but Schur’s result showed that PSL(2, p) required at least three relations. However, the possibility of a 2-generator 2-relation presentation for SL(2, p) was not excluded.
The authors wish to thank the Carnegie Trust for the Universities of Scotland for a grant to assist the work of this paper.
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© 1981 Springer-Verlag New York Inc.
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Campbell, C.M., Robertson, E.F. (1981). Two-Generator Two-Relation Presentations for Special Linear Groups. In: Davis, C., Grünbaum, B., Sherk, F.A. (eds) The Geometric Vein. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5648-9_38
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