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Deficiency zero presentations for certain perfect groups

Published online by Cambridge University Press:  14 November 2011

C. M. Campbell ,
E. F. Robertson ,
T. Kawamata ,
I. Miyamoto  and
P. D. Williams
C. M. Campbell
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16, 9SS, Scotland
E. F. Robertson
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16, 9SS, Scotland
T. Kawamata
Affiliation:
Faculty of Engineering, Yamanashi University, Takeda-4, Kofu, Japan
I. Miyamoto
Affiliation:
Faculty of Engineering, Yamanashi University, Takeda-4, Kofu, Japan
P. D. Williams
Affiliation:
Department of Mathematics, California State University, San Bernardino, CA 92407, U.S.A.
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Synopsis

In this paper we give two generator, two relation presentations for the following perfect groups which were not previously known to have deficiency zero: SL(2, 32), SL(2, 64), SL(2, 27), SL(2, 49), Â7, Ŝz(8), SL(2, 5) × SL(2, 5), SL(2, 5) × SL(2, 25). We also give two generator, two relation presentations for three other finite perfect groups, two having SL(2, 7) as an image and one having SL(2, 5) as an image. We also discuss presentations for certain other perfect groups which were known to have deficiency zero and find some neat new presentations for them.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 1-2 , 1986 , pp. 63 - 71
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

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