Abstract
We find new mixed and unmixed Beauville structures for groups constructed as 2-quotients, i.e. quotients of 2-power order, of the fundamental group of a certain simplicial complex.
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Bauer, I.C., Catanese, F., Grunewald, F.: The classification of surfaces with p g = q = 0 isogenous to a product of curves. Pure Appl. Math. Q. 4(2), part 1, 547–586 (2008)
Bauer, I.C., Catanese, F., Grunewald, F.: Beauville surfaces without real structures, Geometric methods in algebra and number theory. Progr. Math., 235. Birkhauser Boston, Boston, pp. 1–42 (2005)
Bauer I.C., Catanese F., Grunewald F.: Chebycheff and Belyi polynomials, dessins denfants, Beauville surfaces and group theory. Mediterr. J. Math. 3(2), 121–146 (2006)
Bauer, I.C., Catanese, F., Pignatelli, R.: Surfaces of general type with geometric genus zero: a survey (2010). arXiv:1004.2583v1 [math.AG]
Beauville, A.: Surfaces algébriques complexes, Société Mathématique de France, Paris, Avec une sommaire en anglais, Astérisque, no. 54 (1978)
Bosma W., Cannon J., Playoust C.: The Magma algebra system. I. The user language. J. Symbol. Comput. 24(3–4), 235–265 (1997)
Cartwright D.I., Mantero A.M., Steger T., Zappa A.: Groups acting simply transitively on the vertices of a building of type \({\widetilde{A}_{2} }\) . I. Geom. Dedicata 47(2), 143–166 (1993)
Catanese F.: Fibred surfaces, varieties isogenous to a product and related moduli spaces. Amer. J. Math. 122(1), 1–44 (2000)
Conder M.: Hurwitz groups with given centre. Bull. Lond. Math. Soc. 34(6), 725–728 (2002)
Edjvet M., Howie J.: Star graphs, projective planes and free subgroups in small cancellation groups. Proc. London Math. Soc. (3) 57(2), 301–328 (1988)
Fuertes Y., González-Diez G.: On Beauville structures on the groups S n and A n . Math. Z 264(4), 959–968 (2010)
Fuertes, Y., González-Diez, G., Jaikin-Zapirain, A.: On Beauville surfaces.http://www.uam.es/personal_pdi/ciencias/ajaikin/preprints/Beauville.pdf. Accessed May 2010
Fuertes, Y., Jones, G.: Beauville surfaces and finite groups (2009). arXiv:0910.5489v2 [math.GR]
Garion, S.: On Beauville Structures for PSL(2, q) (2010). arXiv:1003.2792v1[math.GR]
Garion, S., Larsen, M., Lubotzky, A.: Beauville surfaces and finite simple groups (2010). arXiv: 1005.2316v1[math.GR]
Garion, S., Penegini, M.: New Beauville surfaces, moduli spacs and finite groups (2009). arXiv: 0910.5402v2[math.GR]
Peyerimhoff, N., Vdovina, A.: Cayley graph expanders and groups of finite width. J. Pure. Appl. Algebra. (2008). arXiv:0809.1560v1[math.GR]
Serrano F.: Isotrivial fibred surfaces. Ann. Mat. Pura Appl. (4) 171(1), 63–81 (1996)
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Communicated by John S. Wilson.
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Barker, N., Boston, N., Peyerimhoff, N. et al. New examples of Beauville surfaces. Monatsh Math 166, 319–327 (2012). https://doi.org/10.1007/s00605-011-0284-6
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DOI: https://doi.org/10.1007/s00605-011-0284-6