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.
Groups whose character degree graph has diameter three / C. Casolo, S. Dolfi, E. Pacifici, L. Sanus. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 215:2(2016 Sep), pp. 523-558. [10.1007/s11856-016-1387-5]
Groups whose character degree graph has diameter three
E. PacificiPenultimo
;
2016
Abstract
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.
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