Abstract
AbstractLetGbe a group. A subsetXofGis a set of pairwise noncommuting elements ifxy≠yxfor any two distinct elementsxandyinX. If |X|≥|Y| for any other set of pairwise noncommuting elementsYinG, thenXis 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 somep-groups of maximal class. Specifically, we determine this cardinality for all 2 -groups and 3 -groups of maximal class.
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