A two-generator presentation for the Picard group
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- by A. M. Brunner PDF
- Proc. Amer. Math. Soc. 115 (1992), 45-46 Request permission
Abstract:
The following $2$-generator $5$-relator presentation is given for the Picard group $\operatorname {PSL} (2,Z(i))$: \[ langle a,w,b;b = a{w^2}{a^{ - 1}}{w^{ - 2}}a{w^2},\ {({a^2}wa{w^{ - 1}})^2} = {(awa{w^{ - 1}})^3} = {(wb)^2} = {(ab)^2} = {b^2} = 1\rangle .\]References
- Andrew M. Brunner, Michael L. Frame, Youn W. Lee, and Norbert J. Wielenberg, Classifying torsion-free subgroups of the Picard group, Trans. Amer. Math. Soc. 282 (1984), no. 1, 205–235. MR 728710, DOI 10.1090/S0002-9947-1984-0728710-2
- Benjamin Fine, The $HNN$ and generalized free product structure of certain linear groups, Bull. Amer. Math. Soc. 81 (1975), 413–416. MR 372059, DOI 10.1090/S0002-9904-1975-13763-3
Additional Information
- © Copyright 1992 American Mathematical Society
- 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