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

We construct a rank $3$ geometry $Γ (O^{'} N)$ over the diagram PICT whose automorphism group is the O’Nan sporadic simple group. The maximal parabolic subgroups are the Janko group $J_{1}$ , $2 \times S_{5}$ and the Mathieu group $M_{11}$ . Our construction is based on a convenient amalgam of known geometries of rank $2$ for $J_{1}$ and $M_{11}$ extracted from the subgroup lattice of $O^{'} N$ .

Keywords

Diagram geometry, coset geometry, sporadic simple groups, O'Nan group, Livingstone graph

Mathematical Subject Classification 2010

Primary: 20D08, 51E24

Milestones

Received: 11 April 2012

Accepted: 13 April 2012

Authors

Thomas Connor

Vol. 13, No. 1, 2013

Thomas Connor

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors