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Cyclic p-groups of symmetries of surfaces

Published online by Cambridge University Press:  18 May 2009

Ravi S. Kulkarni  and
Colin Maclachlan
Ravi S. Kulkarni
Affiliation:
Inst. Mittag-Leffler, Auravägen 17, 5-182 62 Djursholm, Sweden
Colin Maclachlan
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen, Scotland
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Let Σg denote a compact orientable surface of genus g ≥ 2. We consider finite groups G acting effectively on Σg and preserving the orientation—for short, G acts on Σg or Gis a symmetry group of Σg. Each surface Σg admits only finitely many symmetry groups G and the orders of these groups are bounded by Wiman's bound of 84(g – 1). This bound is attained for infinitely many values of g [12], see also [9], and all values of g ≤ 104 for which it is attained are known [4].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 2 , May 1991 , pp. 213 - 221
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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