Maximal non-commuting set in 2-generated p-groups of class two

Abstract

Let [Formula: see text] be a group. A set [Formula: see text] in [Formula: see text] is said to be non-commuting if [Formula: see text] for any two distinct elements [Formula: see text] and [Formula: see text] in [Formula: see text]. If [Formula: see text] for any other non-commuting set [Formula: see text] in [Formula: see text], then [Formula: see text] is said to be a maximal non-commuting set. In this paper, we obtain the cardinality of a maximal non-commuting set in [Formula: see text]-generated [Formula: see text]-groups of class two having finite commutator subgroup.