Finite groups with special Sylow 2-subgroups

Abstract

Let T be a Sylow 2-subgroup of a simple group PSU (3, 2n), and Z a proper subgroup belonging to the center of T. We shall prove that a simple finite group whose Sylow 2-subgroup is isomorphic to T/Z coincides with PSU (3, 2n). As a consequence we list simple groups that can be represented in the form of a product of two Schmidt groups, i.e., of minimal nonnilpotent groups.