On the diameters of McKay graphs for finite simple groups

Martin W. Liebeck; Aner Shalev; Pham Huu Tiep

doi:10.1007/s11856-021-2109-1

On the diameters of McKay graphs for finite simple groups

Martin W. Liebeck, Aner Shalev, Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Let G be a finite group, and α a nontrivial character of G. The McKay graph ℳ(G, α) has the irreducible characters of G as vertices, with an edge from χ₁ to χ₂ if χ₂ is a constituent of αχ₁. We study the diameters of McKay graphs for simple groups G of Lie type. We show that for any α, the diameter is bounded by a quadratic function of the rank, and obtain much stronger bounds for G = PSL_n(q) or PSU_n(q).

Original language	English (US)
Pages (from-to)	449-464
Number of pages	16
Journal	Israel Journal of Mathematics
Volume	241
Issue number	1
DOIs	https://doi.org/10.1007/s11856-021-2109-1
State	Published - Mar 2021

ASJC Scopus subject areas

General Mathematics

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abstract = "Let G be a finite group, and α a nontrivial character of G. The McKay graph ℳ(G, α) has the irreducible characters of G as vertices, with an edge from χ1 to χ2 if χ2 is a constituent of αχ1. We study the diameters of McKay graphs for simple groups G of Lie type. We show that for any α, the diameter is bounded by a quadratic function of the rank, and obtain much stronger bounds for G = PSLn(q) or PSUn(q).",

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AB - Let G be a finite group, and α a nontrivial character of G. The McKay graph ℳ(G, α) has the irreducible characters of G as vertices, with an edge from χ1 to χ2 if χ2 is a constituent of αχ1. We study the diameters of McKay graphs for simple groups G of Lie type. We show that for any α, the diameter is bounded by a quadratic function of the rank, and obtain much stronger bounds for G = PSLn(q) or PSUn(q).

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On the diameters of McKay graphs for finite simple groups

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