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On presentation of PSL (2, pn)

Part of: Representation theory of groups Special aspects of infinite or finite groups Linear algebraic groups and related topics

Published online by Cambridge University Press:  09 April 2009

C. M. Campbell ,
E. F. Robertson  and
P. D. Williams
C. M. Campbell
Affiliation:
University of St. AndrewsNorth Haugh St. Andrews Fife KY 16 9SS, Scotland
E. F. Robertson
Affiliation:
University of St. AndrewsNorth Haugh St. Andrews Fife KY 16 9SS, Scotland
P. D. Williams
Affiliation:
California State University5500 University Parkway San Bernardino, California 92407, U.S.A.
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Abstract

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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 ni. Certain new efficient presentations are given for certain cases of the groups considered.

MSC classification

Secondary: 20F05: Generators, relations, and presentations 20D06: Simple groups 20G40: Linear algebraic groups over finite fields
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 2 , April 1990 , pp. 333 - 346
Copyright
Copyright © Australian Mathematical Society 1990

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