Purely (non-)strongly real Beauville p-groups

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Gül Erdem Ş.

ARCHIV DER MATHEMATIK, vol.115, no.1, pp.1-11, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 115 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1007/s00013-020-01441-8
  • Journal Name: ARCHIV DER MATHEMATIK
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1-11
  • Keywords: Beauville groups, Strongly real Beauville p-groups, Metacyclic p-groups, p-groups of class 2, SURFACES
  • TED University Affiliated: Yes

Abstract

For every prime p >= 5, we give examples of Beauville p-groups whose Beauville structures are never strongly real. This shows that there are nilpotent purely non-strongly real Beauville groups. On the other hand, we determine infinitely many Beauville 2-groups which are purely strongly real. This answers two questions formulated by Fairbairn (Arch Math. https://doi.org/10.1007/s00013-018-1288-4).