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Derived Length and Products of Conjugacy Classes | Edith Adan-Bante
; | Date: |
22 Dec 2006 | Subject: | Group Theory | Abstract: | Let $G$ be a supersolvable group and $A$ be a conjugacy class of $G$. Observe that for some integer $eta(AA^{-1})>0$, $AA^{-1}={a b^{-1}mid a,bin A}$ is the union of $eta(AA^{-1})$ distinct conjugacy classes of $G$. Set ${f C}_G(A)={gin Gmid a^g=a ext{for all} ain A}$. Then the derived length of $G/{f C}_G(A)$ is less or equal than $2eta(A A^{-1})-1$. | Source: | arXiv, math/0612723 | Services: | Forum | Review | PDF | Favorites |
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