Hurwitz小组的最新进展

Groups Complex. Cryptol. Pub Date : 1900-01-01 DOI:10.1515/gcc.2010.002

M. Conder

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引用次数: 50

摘要

Hurwitz群是(2,3,7)三角形群的任意非平凡有限商，即由元素x和y满足x 2 = y 3 = (xy)7 = 1所生成的任意非平凡有限群。每一个这样的群G都是G > 1属的紧Riemann曲面的共形自同构群，具有|G| = 84(G - 1)的性质，这是给定G属的最大可能阶。本文继作者在Bull的简要综述之后，对Hurwitz群的已知情况和相关问题进行了更新。阿米尔。数学。Soc.23(1990)。

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An update on Hurwitz groups

Abstract A Hurwitz group is any non-trivial finite quotient of the (2, 3, 7) triangle group, that is, any non-trivial finite group generated by elements x and y satisfying x 2 = y 3 = (xy)7 = 1. Every such group G is the conformal automorphism group of some compact Riemann surface of genus g > 1, with the property that |G| = 84(g – 1), which is the maximum possible order for given genus g. This paper provides an update on what is known about Hurwitz groups and related matters, following up the author's brief survey in Bull. Amer. Math. Soc.23 (1990).

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Groups Complex. Cryptol.

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