Abstract
Let G be a supersolvable group and A be a conjugacy class of G. Observe that for some integer η(AA −1) > 0, AA −1 = {ab −1: a, b ∈ A} is the union of η(AA −1) distinct conjugacy classes of G. Set C G (A) = {g ∈ G: a g = a for all a ∈ A. Then the derived length of G/C G (A) is less or equal than 2η(AA −1) − 1.
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Adan-Bante, E. Derived length and products of conjugacy classes. Isr. J. Math. 168, 93–100 (2008). https://doi.org/10.1007/s11856-008-1057-3
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DOI: https://doi.org/10.1007/s11856-008-1057-3