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On a graph related to permutability in finite groups. (English)
Ann. Mat. Pura Appl. (4) 189, No. 4, 567-570 (2010).
Summary: For a finite group $G$ we define the graph $Γ(G)$ to be the graph whose vertices are the conjugacy classes of cyclic subgroups of $G$ and two conjugacy classes $\cal A, \cal B$ are joined by an edge if for some $A \in \cal A$, $B \in \cal B$, $A$ and $B$ permute. We characterise those groups $G$ for which $Γ(G)$ is complete.