Fischer graph of a subgroup

Definition with symbols
Let $$A$$ be a subgroup of a group $$G$$, and let $$S$$ be the set of all conjugates of $$A$$. Then the Fischer graph $$\Gamma$$ associated with $$A$$ is defined as follows:


 * Its vertex set is $$S$$ (viz, the vertices are conjugates of $$A$$)
 * Two vertices in $$S$$ are adjacent if they commute element-wise. Viz, $$A$$ and $$B$$ are adjacent if $$[A,B] = 1$$

The group $$G$$ acts on the Fischer graph $$\Gamma$$ by conjugation.

Connected complement
The graph-theoretic complement of the Fischer graph of a contranormal subgroup is connected.