Let G be a group. A subset X of G is a set of pairwise noncommuting elements if x y = yx for any two distinct elements x and y in X . If |X | ≥ |Y | for any other set of pairwise noncommuting elements Y in G, then X is said to be a maximal subset of pairwise noncommuting elements. In this paper we determine the cardinality of a maximal subset of pairwise noncommuting elements for some p-groups of maximal class. Specifically, we determine this cardinality for all 2-groups and 3-groups of maximal class.2010 Mathematics subject classification: primary 20D15; secondary 20D60.
Let G be a finite group. A subset X of G is a set of pairwise noncommuting elements if any two distinct elements of X do not commute. In this paper we determine the maximum size of these subsets in any finite nonabelian metacyclic p-group for an odd prime p.2010 Mathematics subject classification: primary 20D15; secondary 20D60.
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