Purely (non-)strongly real Beauville groups

  • Ben FairbairnEmail author


We discuss Beauville groups whose corresponding Beauville surfaces are either always strongly real or never strongly real producing several infinite families of examples.


Beauville surface Strongly real surface Beauville group 

Mathematics Subject Classification

Primary 20D06 Secondary 14J29 30F10 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



  1. 1.
    Barker, N.W., Bosten, N., Fairbairn, B.T.: A note on Beauville \(p\)-groups. Exp. Math. 21(3), 298–306 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bauer, I., Catanese, F., Grunewald, F.: Beauville surfaces without real structures. In: Bogomolov, F., Tschinkel, Y. (eds.) Geometric Methods in Algebra and Number Theory, Progress in Mathematics, vol. 235, pp. 1–42. Birkhäuser, Boston (2005)CrossRefGoogle Scholar
  3. 3.
    Catanese, F.: Fibered surfaces, varieties isogenous to a product and related moduli spaces. Am. J. Math. 122(1), 1–44 (2000)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Fairbairn, B.T.: Some exceptional Beauville structures. J. Group Theory 15(5), 631–639 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fairbairn, B.T.: Strongly real Beauville groups. In: Bauer, I., Garion, S., Vdovina, A. (eds.) Beauville Surfaces and Groups, Springer Proceedings in Mathematics and Statistics, vol. 123, pp. 41–61. Springer, Berlin (2015)Google Scholar
  6. 6.
    Fairbairn, B.T.: More on strongly real Beauville groups. In: Širáň, J., Jajcay, R. (eds.) Symmetries in Graphs Maps and Polytopes 5th SIGMAP Workshop, West Malvern, UK, July 2014. Springer Proceedings in Mathematics and Statistics, vol. 159, pp. 129–146 (2016)Google Scholar
  7. 7.
    Fairbairn, B.T.: A new infinite family of non-abelian strongly real Beauville \(p\)-groups for every odd prime \(p\). Bull. Lond. Math. Soc. 49(4) (2017)Google Scholar
  8. 8.
    Fernández-Alcober, G.A., Gül, Ş.: Beauville structures in finite \(p\)-groups. J. Algebra 474, 1–23 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Fuertes, Y., González-Diez, G.: On Beauville structures on the groups \(S_n\) and \(A_n\). Math. Z. 264(4), 959–968 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Fuertes, Y., Jones, G.: Beauville surfaces and finite groups. J. Algebra 340, 13–27 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gül, Ş.: A note on strongly real Beauville \(p\)-groups. Preprint arXiv:1607.08907
  12. 12.
    Gül, Ş.: An infinite family of strongly real Beauville \(p\)-groups. Monatsh. Math. 185(4), 663–675 (2018)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Helleloid, G.T., Martin, U.: The automorphism group of a finite \(p\)-group is almost always a \(p\)-group. J. Algebra 312, 284–329 (2007)MathSciNetCrossRefGoogle Scholar
  14. 14.
    MacBeath, A. M.: Generators of the linear fractional groups. In: Number Theory (Proceedings of Symposia in Pure Mathematics, Vol. XII, Houston, Texas, 1967), pp. 14–32. American Mathematical Society, Providence (1969)Google Scholar
  15. 15.
    Stix, J., Vdovina, A.: Series of \(p\)-groups with Beauville structure. Monatsh. Math. 181(1), 177–186 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Economics, Mathematics and StatisticsBirkbeck, University of LondonLondonUK

Personalised recommendations