On the degree of commutativity of p-groups of maximal class

The first major study of p-groups of maximal class was made by Blackburn in 1958. He showed that an important invariant parameter of these groups is its ‘degree of commutativity’, which is a measure of the commutativity among the members of the lower central series of G.In this paper, we find a lower bound for the degree of commutativity of some p-groups of maximal class of order pm, by using m and another two known invariant parameters of a p-group of maximal class. This bound improves the best one given in terms of the order of G.