Derived Length and Products of Conjugacy Classes

Details Derived Length and Products of Conjugacy Classes Derived Length and Products of Conjugacy Classes

2006-12-22

arxiv.org/abs/math/0612723v1

Mathematics

Group Theory

Scientific paper

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 $2\eta(A A^{-1})-1$.

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