Character degree graphs with no complete vertices |
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Authors: | Claudio Paolo Morresi Zuccari |
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Institution: | Dipartimento di Matematica Pura e Applicata, Università dell?Aquila, via Vetoio 1, 67010 Coppito, L?Aquila, Italy |
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Abstract: | Let Γ be a graph in which each vertex is non-adjacent to another different one. We show that, if G is a finite solvable group with abelian Fitting subgroup and with character degree graph , then G is a direct product of subgroups having a disconnected character degree graph. In particular, Γ is a join of disconnected graphs. We deduce also that solvable groups with abelian Fitting subgroup have a character degree graph with diameter at most 2. |
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