On Cyclic Groups of Automorphisms of Riemann Surfaces | Zendy

Bujalance Emilio | Zendy; Conder Marston | Zendy

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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.

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