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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Presentations for $ 3$-dimensional special linear groups over integer rings


Authors: Marston Conder, Edmund Robertson and Peter Williams
Journal: Proc. Amer. Math. Soc. 115 (1992), 19-26
MSC: Primary 20F05; Secondary 20G40
MathSciNet review: 1079696
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Abstract: The following $ 2$-generator $ 6$-relator presentation is obtained for the $ 3$-dimensional special linear group $ \operatorname{SL}(3,{\mathbb{Z}_k})$ for each odd integer $ k > 1$:

$\displaystyle \operatorname{SL}(3,{\mathbb{Z}_k}) = \langle x,y\vert{x^3} = {y^... ...{(x{y^{ - 1}}xyx{y^{ - 1}}{x^{ - 1}}{y^{ - 1}})^{(k - 1)/2}}xy)^4} = 1\rangle .$

Alternative presentations for these groups and other groups associated with them are also given.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1079696-5
PII: S 0002-9939(1992)1079696-5
Article copyright: © Copyright 1992 American Mathematical Society