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On Cyclic Groups of Automorphisms of Riemann Surfaces
Author(s) -
Bujalance Emilio,
Conder Marston
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007115
Subject(s) - automorphism , mathematics , riemann surface , pure mathematics , group (periodic table) , fuchsian group , action (physics) , automorphisms of the symmetric and alternating groups , genus , surface (topology) , outer automorphism group , riemann–hurwitz formula , riemann hypothesis , compact riemann surface , cyclic group , automorphism group , riemann xi function , geometry , physics , botany , quantum mechanics , biology , abelian group
The question of extendability of the action of a cyclic group of automorphisms of a compact Riemann surface is considered. Particular attention is paid to those cases corresponding to Singerman's list of Fuchsian groups which are not finitely‐maximal, and more generally to cases involving a Fuchsian triangle group. The results provide partial answers to the question of which cyclic groups are the full automorphism group of some Riemann surface of given genus g >1.