  A subset X of a group G is a set of pairwise non-commuting ele- ments if ab
6= ba for any two distinct elements a and b in X. If jXj ? jY j 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 and the cardinality of such a subset
is denoted by !(G). In this paper, among other thing, we prove that, for each
positive integer n, there are only finitely many groups G, up to isoclinic,
with !(G) = n (with exactly n centralizers).
