Radical subgroups of the sporadic simple group of Suzuki

Abstract

For the sporadic Suzuki simple group, the radical $p$-subgroups for $p = 2$ and 3 are classified and the simplicial complex of their chains is shown to be homotopically equivalent to a $p$-local geometry. Further investigation of the related complexes for $p = 2$ gives a counterexample to Conjecture 1 in [4].