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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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