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On conjugacy classes and derived length | Edith Adan-Bante
; | Date: |
8 May 2009 | Abstract: | Let $G$ be a finite group and $A$, $B$ and $D$ be conjugacy classes of $ G$
with $Dsubseteq AB={xymid xin A, yin B}$. Denote by $eta(AB)$ the number
of distinct conjugacy classes such that $AB$ is the union of those. Set ${f
C}_G(A)={gin Gmid x^g=x {for all} xin A}$. If $AB=D$ then ${f
C}_G(D)/({f C}_G(A)cap{f C}_G(B))$ is an abelian group. If, in addition,
$G$ is supersolvable, then the derived length of ${f C}_G(D)/({f
C}_G(A)cap{f C}_G(B))$ is bounded above by $2eta(AB)$. | Source: | arXiv, 0905.1342 | Services: | Forum | Review | PDF | Favorites |
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