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| Volume 34 • Number 3 • 2011 |
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On a Graph Associated to Groups
Mohammad Mashkouri and Bijan Taeri
Abstract.
Let G be a group such that the subgroup T2(G)={x∈G∣(gx)2=(xg)2, for all g∈G} is a proper subgroup. We define a graph Γ with the vertex set G∖T2(G) in which two vertices x,y are joined by an edge if (xy)2≠(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.
Full text: PDF
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