An amalgam uniqueness result for recognising q6:SU3(q), G2(q), or 3˙M10 using biaffine polar spaces

Justin McInroy*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)


A biaffine polar space is formed by removing two hyperplanes, one from the polar space and one from the dual polar space. We describe two similar examples of these over a general field, each with the automorphism group acting flag-transitively. The stabilisers of certain flags are isomorphic in each geometry, hence they have similar amalgams. We classify such amalgams over finite fields, showing that only these two cases can occur when q not equal 2 and that they differ by whether certain subgroups commute. This leads to a recognition theorem for q6:SU3(q), or G2(q), for q not equal 2, with a third possibility 3˙M10 when q = 2.
Original languageEnglish
Pages (from-to)105-122
Number of pages18
JournalJournal of Algebra
Early online date20 Dec 2013
Publication statusPublished - 15 Feb 2014


  • Amalgam
  • Recognition theorem
  • Mathieu
  • Biaffine
  • G_2
  • Hyperplane
  • Polar space
  • Diagram geometry

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