A geometric characterization of the groups \(M_{12}\), \(He\) and \(Ru\) (Q1184414)

Amongst other things, the author determines the flag-transitive automorphism groups of such extended generalized octagons in which triples of pairwise collinear points exist which do not lie on any circle and which satisfy certain additional assumptions on the point-residues. The simple groups involved in these automorphism groups are \(L_ 3(4)\), \(M_{12}\), \(He\), and \(Ru\).