The normal subgroup structure of the Picard group
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- by Benjamin Fine and Morris Newman PDF
- Trans. Amer. Math. Soc. 302 (1987), 769-786 Request permission
Abstract:
The Picard group $\Gamma$ is $PS{L_2}(Z[i])$, the group of linear fractional transformations with Gaussian integer coefficients. We examine the structure of the normal subgroups of $\Gamma$. In particular we give a complete classification of the normal subgroups for indices less than $60$ and show that beyond this there are large gaps in the possible indices. This classification depends on the structure of the derived series. Finally we give examples of normal noncongruence subgroups.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 302 (1987), 769-786
- MSC: Primary 20H05; Secondary 11F06, 22E40
- DOI: https://doi.org/10.1090/S0002-9947-1987-0891646-3
- MathSciNet review: 891646