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Maximal symmetry and fully wound coverings


Author: Coy L. May
Journal: Proc. Amer. Math. Soc. 79 (1980), 23-31
MSC: Primary 14H99; Secondary 14H30
DOI: https://doi.org/10.1090/S0002-9939-1980-0560577-X
MathSciNet review: 560577
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Abstract: A compact bordered Klein surface of genus $ g \geqslant 2$ is said to have maximal symmetry if its automorphism group is of order $ 12(g - 1)$, the largest possible. We show that for each value of k there are only finitely many topological types of bordered Klein surfaces with maximal symmetry that have exactly k boundary components. We also prove that there are no bordered Klein surfaces with maximal symmetry that have exactly p boundary components for any prime $ p \geqslant 5$. These results are established using the concept of a fully wound covering, that is, a full covering $ \varphi :X \to Y$ of the bordered surface Y with the maximum possible boundary degree.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0560577-X
Keywords: Bordered Klein surface, genus, automorphism, maximal symmetry, full covering, fully wound covering, boundary degree, $ {M^ \ast }$-group, regular map
Article copyright: © Copyright 1980 American Mathematical Society

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