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On non-abelian strongly real Beauville $p$-groups

Year 2025, Volume: 54 Issue: 5, 1839 - 1844, 29.10.2025
https://doi.org/10.15672/hujms.1411816

Abstract

We give an infinite family of non-abelian strongly real Beauville $p$-groups for any odd prime $p$ by considering the lower central quotients of the free product of two cyclic groups of order $p$.

References

  • [1] R. Camina, The Nottingham group, in New Horizons in Pro-p Groups, editors M. du Sautoy, D. Segal, A. Shalev, Progress in Mathematics, Volume 184, Birkhäuser, pp. 205–221, 2000.
  • [2] F. Catanese, Fibred surfaces, varieties isogenous to a product and related moduli spaces, Amer. J. Math. 122, 1–44, 2000.
  • [3] T.E. Easterfield, The orders of products and commutators in prime power groups, Proc. Cambridge Phil. Soc. 36, 14–26, 1940.
  • [4] B. Fairbairn, More on strongly real Beauville groups, in Symmetries in Graphs, Maps, and Polytopes, editors J. Siran, R. Jajcay, Springer Proceedings in Mathematics & Statistics, Volume 159, Springer, pp. 129–146, 2016.
  • [5] B. Fairbairn, A new infinite family of non-abelian strongly real Beauville p-groups for every odd prime p, Bull. London Math. Soc. 49(5), 749-754, 2017.
  • [6] G.A. Fernández-Alcober and Ş. Gül, Beauville structures in finite p-groups, J. Algebra 474, 1–23, 2017.
  • [7] Ş. Gül, Beauville structures in p-central quotients, J. Group Theory 20, 257-267, 2017.
  • [8] Ş. Gül, An infinite family of strongly real Beauville p-groups, Monatsh. Math. 185, 663-675, 2018.
  • [9] D. F. Holt, B. Eick, and E. A. O’brien, Handbook of Computational Group Theory, Chapman & Hall/CRC Press, 2005.
  • [10] B. Huppert and N. Blackburn, Finite Groups II , Springer-Verlag, Berlin, 1982.
  • [11] B. Klopsch, Automorphisms of the Nottingham group, J. Algebra 223, 37–56, 2000.
  • [12] C. R. Leedham Green and S. McKay, The Structure of Groups of Prime Power Order, London Math. Soc. Monographs, New Ser. 27, 2002.

Year 2025, Volume: 54 Issue: 5, 1839 - 1844, 29.10.2025
https://doi.org/10.15672/hujms.1411816

Abstract

References

  • [1] R. Camina, The Nottingham group, in New Horizons in Pro-p Groups, editors M. du Sautoy, D. Segal, A. Shalev, Progress in Mathematics, Volume 184, Birkhäuser, pp. 205–221, 2000.
  • [2] F. Catanese, Fibred surfaces, varieties isogenous to a product and related moduli spaces, Amer. J. Math. 122, 1–44, 2000.
  • [3] T.E. Easterfield, The orders of products and commutators in prime power groups, Proc. Cambridge Phil. Soc. 36, 14–26, 1940.
  • [4] B. Fairbairn, More on strongly real Beauville groups, in Symmetries in Graphs, Maps, and Polytopes, editors J. Siran, R. Jajcay, Springer Proceedings in Mathematics & Statistics, Volume 159, Springer, pp. 129–146, 2016.
  • [5] B. Fairbairn, A new infinite family of non-abelian strongly real Beauville p-groups for every odd prime p, Bull. London Math. Soc. 49(5), 749-754, 2017.
  • [6] G.A. Fernández-Alcober and Ş. Gül, Beauville structures in finite p-groups, J. Algebra 474, 1–23, 2017.
  • [7] Ş. Gül, Beauville structures in p-central quotients, J. Group Theory 20, 257-267, 2017.
  • [8] Ş. Gül, An infinite family of strongly real Beauville p-groups, Monatsh. Math. 185, 663-675, 2018.
  • [9] D. F. Holt, B. Eick, and E. A. O’brien, Handbook of Computational Group Theory, Chapman & Hall/CRC Press, 2005.
  • [10] B. Huppert and N. Blackburn, Finite Groups II , Springer-Verlag, Berlin, 1982.
  • [11] B. Klopsch, Automorphisms of the Nottingham group, J. Algebra 223, 37–56, 2000.
  • [12] C. R. Leedham Green and S. McKay, The Structure of Groups of Prime Power Order, London Math. Soc. Monographs, New Ser. 27, 2002.
There are 12 citations in total.

Details

Primary Language English
Subjects Group Theory and Generalisations
Journal Section Mathematics
Authors

Şükran Gül 0000-0003-4792-7084

Early Pub Date April 11, 2025
Publication Date October 29, 2025
Submission Date December 29, 2023
Acceptance Date February 14, 2025
Published in Issue Year 2025 Volume: 54 Issue: 5

Cite

APA Gül, Ş. (2025). On non-abelian strongly real Beauville $p$-groups. Hacettepe Journal of Mathematics and Statistics, 54(5), 1839-1844. https://doi.org/10.15672/hujms.1411816
AMA Gül Ş. On non-abelian strongly real Beauville $p$-groups. Hacettepe Journal of Mathematics and Statistics. October 2025;54(5):1839-1844. doi:10.15672/hujms.1411816
Chicago Gül, Şükran. “On Non-Abelian Strongly Real Beauville $p$-Groups”. Hacettepe Journal of Mathematics and Statistics 54, no. 5 (October 2025): 1839-44. https://doi.org/10.15672/hujms.1411816.
EndNote Gül Ş (October 1, 2025) On non-abelian strongly real Beauville $p$-groups. Hacettepe Journal of Mathematics and Statistics 54 5 1839–1844.
IEEE Ş. Gül, “On non-abelian strongly real Beauville $p$-groups”, Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 5, pp. 1839–1844, 2025, doi: 10.15672/hujms.1411816.
ISNAD Gül, Şükran. “On Non-Abelian Strongly Real Beauville $p$-Groups”. Hacettepe Journal of Mathematics and Statistics 54/5 (October2025), 1839-1844. https://doi.org/10.15672/hujms.1411816.
JAMA Gül Ş. On non-abelian strongly real Beauville $p$-groups. Hacettepe Journal of Mathematics and Statistics. 2025;54:1839–1844.
MLA Gül, Şükran. “On Non-Abelian Strongly Real Beauville $p$-Groups”. Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 5, 2025, pp. 1839-44, doi:10.15672/hujms.1411816.
Vancouver Gül Ş. On non-abelian strongly real Beauville $p$-groups. Hacettepe Journal of Mathematics and Statistics. 2025;54(5):1839-44.