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Low rank groups of Lie type acting point and line-primitively on finite generalised quadrangles
Vishnuram Arumugam, John Bamberg, Michael Giudici
Suppose we have a finite thick generalised quadrangle whose automorphism group acts primitively on both the set of points and the set of lines. Then must be almost simple.…
Tactical decompositions in finite polar spaces and non-spreading classical group actions
John Bamberg, Michael Giudici, Jesse Lansdown +1
For finite classical groups acting naturally on the set of points of their ambient polar spaces, the symmetry properties of \emph{synchronising} and \emph{separating} are equivalen…
New 2-closed groups that are not automorphism groups of digraphs
John Bamberg, Michael Giudici, Jacob Paul Smith
In this paper we extend the construction of Giudici, Morgan and Zhou [arXiv:2110.07896] to give the first known examples of nonregular, -closed permutation groups of rank greate…
Spreading primitive groups of diagonal type do not exist
John Bamberg, Saul D. Freedman, Michael Giudici
The synchronisation hierarchy of finite permutation groups consists of classes of groups lying between 2-transitive groups and primitive groups. This includes the class of spreadin…