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Volume 34 • Number 3 • 2011
• On a Graph Associated to Groups
Mohammad Mashkouri and Bijan Taeri

Let $G$ be a group such that the subgroup $T^2(G)=\{x\in G\mid (gx)^2=(xg)^2, \ \mbox{for all }\ g\in G\}$ is a proper subgroup. We define a graph $\Gamma$ with the vertex set $G\setminus T^2(G)$ in which two vertices $x,y$ are joined by an edge if $(xy)^2\neq (yx)^2$. In this note we study this graph and find a characterization of some dihedral groups in terms of this graph.

2010 Mathematics Subject Classification: 20D60, 05C25.

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