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

 

A two-generator presentation for the Picard group


Author: A. M. Brunner
Journal: Proc. Amer. Math. Soc. 115 (1992), 45-46
MSC: Primary 20F05
MathSciNet review: 1079886
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Abstract: The following $ 2$-generator $ 5$-relator presentation is given for the Picard group $ \operatorname{PSL} (2,Z(i))$:

$\displaystyle langle a,w,b;b = a{w^2}{a^{ - 1}}{w^{ - 2}}a{w^2},\ {({a^2}wa{w^{ - 1}})^2} = {(awa{w^{ - 1}})^3} = {(wb)^2} = {(ab)^2} = {b^2} = 1\rangle.$


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1079886-1
PII: S 0002-9939(1992)1079886-1
Article copyright: © Copyright 1992 American Mathematical Society