Commutators in groups of order p7

Abstract

In this paper, we present a characterization of groups [Formula: see text] of order [Formula: see text], [Formula: see text] prime, in which not all elements of the commutator subgroup [Formula: see text] of [Formula: see text] are commutators in [Formula: see text]. In the way, we obtain several structural results on groups of order [Formula: see text].