On the Planarity of a Graph Related to the Join of Subgroups of a Finite Group

نویسندگان

  • H. AHMADI
  • Ali Reza Ashrafi
چکیده

Let G be a finite group which is not a cyclic p-group, p a prime number. We define an undirected simple graph ∆(G) whose vertices are the proper subgroups of G, which are not contained in the Frattini subgroup of G and two vertices H and K are joined by an edge if and only if G = ⟨H,K⟩. In this paper we classify finite groups with planar graph. Our result shows that only few groups have planar graphs.

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تاریخ انتشار 2014