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<p>Let <i>G</i> be a finite group and <i>π</i>(<i>G</i>) be the set of prime divisors of ∣<i>G</i>∣. The prime graph Γ(<i>G</i>) of <i>G</i> is the graph with vertex set <i>π</i>(<i>G</i>), and different <i>p, q</i> ∈ <i>π</i>(<i>G</i>) are joined by an edge if and only if <i>G</i> has an element of order <i>pq</i>. In this paper, we characterize the finite solvable groups whose prime graphs have diameter 3.</p>

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Finite Solvable Groups Whose Prime Graphs have Diameter 3

  • 期刊论文

  • 发表日期：

    2025年3月15日

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  • Guohua Qian

摘要

Let G be a finite group and π(G) be the set of prime divisors of ∣G∣. The prime graph Γ(G) of G is the graph with vertex set π(G), and different p, q ∈ π(G) are joined by an edge if and only if G has an element of order pq. In this paper, we characterize the finite solvable groups whose prime graphs have diameter 3.