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


Nilpotent automorphism groups of Riemann surfaces

Author: Reza Zomorrodian
Journal: Trans. Amer. Math. Soc. 288 (1985), 241-255
MSC: Primary 20H10; Secondary 14H45, 20D45, 30F10
MathSciNet review: 773059
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Abstract: The action of nilpotent groups as automorphisms of compact Riemann surfaces is investigated. It is proved that the order of a nilpotent group of automorphisms of a surface of genus $ g \geqslant 2$ cannot exceed $ 16(g - 1)$. Exact conditions of equality are obtained. This bound corresponds to a specific Fuchsian group given by the signature (0;2,4,8).

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Additional Information

PII: S 0002-9947(1985)0773059-6
Keywords: Fuchsian groups, nilpotent automorphism groups, compact Riemann surfaces, action of groups, generators, relations, signatures, bounds, maximal order of groups
Article copyright: © Copyright 1985 American Mathematical Society

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