Some rank six geometries for the smallest Fischer sporadic simple group

Moshtagh, Hossein; Rahimipour, Ali Reza

doi:10.22061/jdma.2025.11584.1111

Some rank six geometries for the smallest Fischer sporadic simple group

Document Type : Full Length Article

Authors

¹ Department of Computer Science, University of Garmsar, Address Garmsar, Semnan 3588115589, Iran

² Faculty of Electrical & Computer Engineering,, Iran., Malek Ashtar University of Technology, Tehran

10.22061/jdma.2025.11584.1111

Abstract

This paper introduces some new rank six geometries associated with the Fischer sporadic simple group Fi22. These geometries are both residually connected and firm, with Fi22 acts as a
flag-transitive automorphism group on them. The previously known geometries for Fischer sporadic
simple group Fi22 have rank at most four. Therefore, we investigate improvements to the lower bound
of the maximum rank of the residually connected and firm geometries on which the group Fi22 acts
as a flag-transitive automorphism group. Moreover, we demonstrate that the independent generating
set of Fischer sporadic simple group Fi22 has a size of at least seven.

Graphical Abstract