On B( 5, 20) 2-Groups

A finite group [Formula: see text] is said to be a [Formula: see text] group if for any [Formula: see text]-element subset [Formula: see text] of [Formula: see text], [Formula: see text]. It is of interest to characterize the structure of [Formula: see text] groups for [Formula: see text]. The [Formula: see text] groups for [Formula: see text] have been investigated by several authors. In this paper, we give a complete characterization of [Formula: see text] 2-groups by showing there are five classes of such groups which are nontrivial and nonabelian.