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

Abstract

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