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.
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Alhassan et al. (2024) studied this question.
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