Maximal symmetry and fully wound coverings

May, Coy L.

doi:10.1090/S0002-9939-1980-0560577-X

Maximal symmetry and fully wound coverings
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by Coy L. May

Proc. Amer. Math. Soc. 79 (1980), 23-31

DOI: https://doi.org/10.1090/S0002-9939-1980-0560577-X

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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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