On the Planarity of a Graph Related to the Join of Subgroups of a Finite Group
نویسندگان
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.
منابع مشابه
On the planarity of a graph related to the join of subgroups of a finite group
Let $G$ be a finite group which is not a cyclic $p$-group, $p$ a prime number. We define an undirected simple graph $Delta(G)$ 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 $G=langle H , Krangle$. In this paper we classify finite groups with planar graph. ...
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