Abstract
For a finite nonabelian group G, let be the smallest integer m such that G contains m proper centralizers with property In this article, we find for some groups of interest. For two isoclinic groups G1 and G2, we prove that Also we give an upper bound for and determine groups for which this bound is sharp. We investigate groups G for which where is the minimum size of a maximal subset of pairwise non-commuting elements of a group G.
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