MAXIMAL SUBSETS OF PAIRWISE NON-COMMUTING ELEMENTS OF SOME FINITE p-GROUPS

Let G be a group. A subset X of G is a set of pairwise non-commuting elements if xy 6= yx for any two distinct elements x and y in X. If |X| ≥ |Y| for any other set of pairwise non-commuting elements, Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. Here, we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian p-groups with central quotient of order less than or equal to p^3 for any prime number p. As an immediate consequence, we give this cardinality for any non-abelian group of order p^4.