Maximal subsets of pairwise non-commuting elements of some finite p-groups

Abstract

Let G be a group. A subset X of G is a set of pairwise noncommuting <br />elements if xy ̸= yx for any two distinct elements x and y in X. <br />If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, <br />then X is said to be a maximal subset of pairwise non-commuting elements. <br />In this paper we determine the cardinality of a maximal subset of pairwise <br />non-commuting elements in any non-abelian p-groups with central quotient <br />of order less than or equal to p3 for any prime number p. As an immediate <br />consequence we give this cardinality for any non-abelian group of order p4.