%0 Journal Article
%T Derived Length and Products of Conjugacy Classes
%A Edith Adan-Bante
%J Mathematics
%D 2006
%I arXiv
%X Let $G$ be a supersolvable group and $A$ be a conjugacy class of $G$. Observe that for some integer $\eta(AA^{-1})>0$, $AA^{-1}=\{a b^{-1}\mid a,b\in A\}$ is the union of $\eta(AA^{-1})$ distinct conjugacy classes of $G$. Set ${\bf C}_G(A)=\{g\in G\mid a^g=a\text{for all} a\in A\}$. Then the derived length of $G/{\bf C}_G(A)$ is less or equal than $2\eta(A A^{-1})-1$.
%U http://arxiv.org/abs/math/0612723v1