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Symmetries of surfaces: an extension of Kulkarni's theorem

Published online by Cambridge University Press:  18 May 2009

Gareth A. Jones
Gareth A. Jones
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO9 5NH, England
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In [6] Kulkarni considered the set of values of g for which a given finite group G acts faithfully as a group of orientation-preserving self-homeomorphisms of a compact, connected, orientable surface σg of genus g. Let us denote this set by (G). Then Kulkarni showed that there exists a positive integer Kdepending only on the order d = |G| of G, the exponent e= exp G of G and the structure of a Sylow 2-subgroup G2 of G, satisfying:

Theorem 1. (Kulkarni [6]) (G) consists of all but finitely many non-negative integers g ≡ 1 mod K.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 2 , May 1994 , pp. 173 - 184
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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