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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The number of groups of a given genus
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by T. W. Tucker
Trans. Amer. Math. Soc. 258 (1980), 167-179
DOI: https://doi.org/10.1090/S0002-9947-1980-0554326-3

Abstract:

It is shown that the number of groups with a given genus greater than one is finite. The proof depends heavily on V. K. Proulx’s classification of groups of genus one. The key observation is that as the number of vertices of a graph imbedded on a given surface increases, the average face size of the imbedding approaches the average face size of a toroidal imbedding. The result appears to be related to Hurwitz’s theorem bounding the order of a group of conformal automorphisms on a Riemann surface of genus g.
References
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Bibliographic Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 258 (1980), 167-179
  • MSC: Primary 05C10; Secondary 05C25
  • DOI: https://doi.org/10.1090/S0002-9947-1980-0554326-3
  • MathSciNet review: 554326