On geometries of the Conway group Co 3 and their McLaughlin group subgeometries

Abstract Recently, the author published a book [A. A. Ivanov, Ever-Evolving Groups—an Introduction to Modern Finite Group Theory , Algebr. Appl. 32, Springer, Cham, 2025] where he summarised the recent progress in the geometric theory of sporadic groups and outlined some geometries which require further investigation. Among them was a geometry for the smallest Conway sporadic simple group <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>Co</m:mi> <m:mn>3</m:mn> </m:msub> </m: