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A two-generator presentation for the Picard group


Author: A. M. Brunner
Journal: Proc. Amer. Math. Soc. 115 (1992), 45-46
MSC: Primary 20F05
DOI: https://doi.org/10.1090/S0002-9939-1992-1079886-1
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))$:

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


References [Enhancements On Off] (What's this?)

  • [1] A. M. Brunner, M. L. Frame, Y. W. Lee, and N. J. Wielenberg, Classifying torsion-free subgroups of the Picard group, Trans. Amer. Math. Soc. 282 (1984), 205-235. MR 728710 (85h:57012)
  • [2] Benjamin Fine, The HNN and generalized free product structure of certain linear groups, Bull. Amer. Math. Soc. 81 (1975), 413-416. MR 0372059 (51:8276)

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DOI: https://doi.org/10.1090/S0002-9939-1992-1079886-1
Article copyright: © Copyright 1992 American Mathematical Society

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