The Groups of Strong Symmetric Genus 4

• Autores: J. Zimmerman, Coy L. May
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 1, 2005, págs. 21-36
• Idioma: inglés
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• Resumen

  • Let G be a finite group. The strong symmetric genus is the minimum genus of any Riemann surface on which G acts preserving orientation. The groups of strong symmetric genus 3 or less have been classified. Here we classify the groups of strong symmetric genus four. There are exactly ten such groups; eight of these are automorphism groups of regular maps of genus 4.

    We also consider non-abelian p-groups that have an element of maximal possible order. We complete the determination of the strong symmetric genus of each p-group with this property. Conversely, the non-abelian 2-groups of even positive strong symmetric genus have an element of maximum possible order. Further, we establish that for an odd prime p, the strong symmetric genus of a non-abelian p-group is congruent to one modulo a power of p.