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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The normal subgroup structure of the Picard group


Authors: Benjamin Fine and Morris Newman
Journal: Trans. Amer. Math. Soc. 302 (1987), 769-786
MSC: Primary 20H05; Secondary 11F06, 22E40
MathSciNet review: 891646
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0891646-3
PII: S 0002-9947(1987)0891646-3
Keywords: Picard group, congruence subgroup, derived series
Article copyright: © Copyright 1987 American Mathematical Society