Some rank six geometries for the smallest Fischer sporadic simple group

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 aflag-transitive automorphism group on them. The previously known geometries for Fischer sporadicsimple group Fi22 have rank at most four. Therefore, we investigate improvements to the lower boundof the maximum rank of the residually connected and firm geometries on which the group Fi22 actsas a flag-transitive automorphism group. Moreover, we demonstrate that the independent generatingset of Fischer sporadic simple group Fi22 has a size of at least seven.

Some rank six geometries for the smallest Fischer sporadic simple group Keywords:

Sporadic simple group , Coset geometry , Independent generating set