Vol. 13, No. 1, 2013

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A rank 3 geometry for the O'Nan group connected with the Livingstone graph

Thomas Connor

Vol. 13 (2013), No. 1, 83–95

We construct a rank 3 geometry Γ(ON) over the diagram PICT whose automorphism group is the O’Nan sporadic simple group. The maximal parabolic subgroups are the Janko group J1, 2 × S5 and the Mathieu group M11. Our construction is based on a convenient amalgam of known geometries of rank 2 for J1 and M11 extracted from the subgroup lattice of ON.

Diagram geometry, coset geometry, sporadic simple groups, O'Nan group, Livingstone graph
Mathematical Subject Classification 2010
Primary: 20D08, 51E24
Received: 11 April 2012
Accepted: 13 April 2012
Thomas Connor