Publication: Bordered and unbordered Klein surfaces with maximal symmetry
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Publication Date
1986
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Elsevier Science B.V. (North-Holland)
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Abstract
A compact Klein surface with boundary of algebraic genus g≥2 has at most 12(g−1) automorphisms. When a surface attains this bound we say that it has maximal symmetry, and the group of automorphisms is then an M group. In this paper we exhibit four new infinite families of M simple groups, and determine with the aid of a computer the groups PSL(n, q) of order less than 50,000 that are M groups. Using these results, we prove the existence of seven topologically different surfaces of algebraic genus 1013, all of them having maximal symmetry.