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2019-11-12
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info:eu-repo/semantics/openAccess
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London Mathematical Society
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Resumen
A compact Riemann surface is called pseudo-real if it admits anti-conformal (orientationreversing) automorphisms, but no anti-conformal automorphism of order 2. In this paper, we consider upper bounds on the order of a group G of automorphisms of a pseudo-real surface S of given genus g > 1, in general and for certain special cases. We determine for all g 2 the orders of the largest cyclic group and the largest abelian group of automorphisms of a pseudo-real surface of genus g, containing orientation-reversing elements, and consider the problem of finding similar bounds when the group contains no orientation-reversing elements. For arbitrary groups, we show that if M(g) is the order of the largest group of automorphisms of a pseudo-real surface of genus g, then M(g) 2g for every even g 2, while M(g) 4(g − 1) for every odd g 3, and we prove that the latter bound is sharp for a very large and possibly infinite set of odd values of g 3. We also give the precise values of M(g) for all g between 2 and 128, together with the signatures for the actions of the corresponding groups of largest order.
Descripción
This is an Accepted Manuscript of an article published by London Mathematical Society
in "Journal of the London Mathematical Society (2) 101(2), (2020), 877–906", available at: https://doi.org/10.1112/jlms.12296
Este es el manuscrito aceptado del artículo publicado por London Mathematical Society en "Journal of the London Mathematical Society (2) 101(2), (2020), 877–906", disponible en línea: https://doi.org/10.1112/jlms.12296
Este es el manuscrito aceptado del artículo publicado por London Mathematical Society en "Journal of the London Mathematical Society (2) 101(2), (2020), 877–906", disponible en línea: https://doi.org/10.1112/jlms.12296
Categorías UNESCO
Palabras clave
30F10 (primary), 14F37, 20B25, 20H10 (secondary)
Citación
Bujalance, E., Cirre, F.J., Conder, M.D.E. (2020): Bounds on the orders of groups of automorphisms of a pseudo-real surface of given genus. Journal of the London Mathematical Society (2) 101(2), 877–906. https://doi.org/10.1112/jlms.12296
Centro
Facultad de Ciencias
Departamento
Matemáticas Fundamentales
Grupo de investigación
Superficies de Riemann y de Klein