On the Groups with the Particular Non-commuting Graphs
نویسنده
چکیده
Let G be a non-abelian finite group. In this paper, we prove that Γ(G) is K4-free, if and only if G ∼= A× P , where A is an abelian group, P is a 2-group and G/Z(G) ∼= Z2 × Z2. Also, we show that Γ(G) is K1,3-free if and only if G ∼= S3, D8 or Q8.
منابع مشابه
ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS
Let $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ or $Q_8$.
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