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Groups whose character degree graph has diameter three

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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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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica U. Dini, Università degli Studi di Firenze, viale Morgagni 67/a, 50134, Firenze, Italy

    Carlo Casolo & Silvio Dolfi

  2. Dipartimento di Matematica F. Enriques, Università degli Studi di Milano, via Saldini 50, 20133, Milano, Italy

    Emanuele Pacifici

  3. Departament de Matemàtiques, Facultat de Matemàtiques Universitat de València, 46100, Burjassot, València, Spain

    Lucia Sanus

Authors
  1. Carlo Casolo
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  2. Silvio Dolfi
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  3. Emanuele Pacifici
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  4. Lucia Sanus
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Corresponding author

Correspondence to Carlo Casolo.

Additional information

Dedicated to the memory of Laci Kovács

The first three authors are partially supported by the Italian INdAM-GNSAGA.

The fourth author is partially supported by the Spanish MINECO proyecto MTM2013-40464-P, partly with FEDER funds and Prometeo2011/030-Generalitat Valenciana.

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Casolo, C., Dolfi, S., Pacifici, E. et al. Groups whose character degree graph has diameter three. Isr. J. Math. 215, 523–558 (2016). https://doi.org/10.1007/s11856-016-1387-5

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  • DOI: https://doi.org/10.1007/s11856-016-1387-5

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