Regular subgroups of the affine group with no translations

Marco Antonio Pellegrini, Maria Clara Tamburini Bellani

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Given a regular subgroup R of AGLn(F), one can ask if R contains nontrivial translations. A negative answer to this question was given by Liebeck, Praeger and Saxl for AGL2(p) (p a prime), AGL3(p) (p odd) and for AGL4(2). A positive answer was given by Hegedűs for AGLn(p) when n≥4 if p is odd and for n=3 or n≥5 if p=2. A first generalization to finite fields of Hegedűs’ construction was recently obtained by Catino, Colazzo and Stefanelli. In this paper we give examples of such subgroups in AGLn(F) for any n≥5 and any field F. For n<5 we provide necessary and sufficient conditions for their existence, assuming R to be unipotent if charF=0
Original languageEnglish
Pages (from-to)410-418
Number of pages9
JournalJournal of Algebra
Volume478
DOIs
Publication statusPublished - 2017

Keywords

  • Affine group
  • Regular subgroup
  • Translations

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