The Möbius function of PSU(3, 2^{2^n})

Abstract

Let G be the simple group PSU(3, 2 2 n ) , n > 0 . For any subgroup H of G , we compute the Mobius function μ L ( H , G ) of H in the subgroup lattice L of G , and the Mobius function μ L ([ H ], [ G ]) of [ H ] in the poset L of conjugacy classes of subgroups of G . For any prime p , we provide the Euler characteristic of the order complex of the poset of non-trivial p -subgroups of G .