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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Article copyright: © Copyright 1992 American Mathematical Society