2016/07/18 by Carlo Casolo, Casolo, Carlo, Silvio Dolfi +5
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #Coding theory and cryptography #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1607.05038
Let \(G\) be a finite group, and let \(Δ(G)\) denote the prime graph built on the set of degrees of the irreducible complex characters of \(G\). It is well known that, whenever \(Δ(G)\) is connected, the diameter of \(Δ(G)\) is at most \(3\). In the present paper, we provide a description of the finite solvable groups for which the diameter of this graph attains the upper bound. This also enables us to confirm a couple of conjectures proposed by M.L. Lewis.