J Austral Math Soc Ser A 48 pp333--346, 1990.

On Presentations of PSL(2, pⁿ)

C. M. Campbell, E. F. Robertson and P. D. Williams

Abstract

We give presentations for the groups PSL(2, pⁿ), p prime, which show that the deficiency of these groups is bounded below. In particular, for p = 2 where SL(2, 2ⁿ) = PSL(2, 2ⁿ), we show that these groups have deficiency greater than or equal to -2. We give deficiency -1 presentations for direct products of SL(2, 2ⁿ) for coprime n_i. Certain new efficient presentations are given for certain cases of the groups considered.

1980 AMS Subject Classification (1985 Revision): 20F05; secondary 20D06, 20G40

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Authors

C. M. Campbell

University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, Scotland.

E. F. Robertson

University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, Scotland.

P. D. Williams

California State University, 5500 University Parkway, San Bernardino, California 92407, U.S.A.