On maximal subsets in p-groups whose distict elements do not commute

Let G be a finite group. A subset X of G is called a set of pairwise non-commuting elements if xy ≠ yx for all distinct x,y ϵ X. if lxl ≥ lyl for any other subset Y of pairwise non-commuting elements, then X is called a maximal subset of pairwise non-commuting elements and the size of such set is denoted by ω(G). In a recent article by Azad [۵] the value of ω(G) for a certain p−group G is computed and in the present paper our aim is to generalize their result. We also extend our result to find ω(G) for some p−groups of interest.