Rank Three Residually Connected Geometries for $M_{22}$, Revisited

Abstract

The rank $3$ residually connected flag transitive geometries $\Gamma$ for $M_{22}$ for which the stabilizer of each object in $\Gamma$ is a maximal subgroup of $M_{22}$ are determined. As a result this deals with the infelicities in Theorem $3$ of Kilic and Rowley [On rank 2 and rank 3 residually connected geometries for $M_{22}$. Note di Matematica, 22(2003), 107–154].