Bounds on the orders of groups of automorphisms of a pseudo-real surface of given genus

Bujalance García, EmilioCirre Torres, Francisco JavierConder, Marston D. E.2025-12-192025-12-192019-11-12Bujalance, 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.122960024-6107https://doi.org/10.1112/jlms.12296https://hdl.handle.net/20.500.14468/31244This 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.12296Este 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.12296A 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.eninfo:eu-repo/semantics/openAccess1204 GeometríaBounds on the orders of groups of automorphisms of a pseudo-real surface of given genusartículo30F10 (primary)14F3720B2520H10 (secondary)1469-7750