TY - JOUR
T1 - On the diameters of McKay graphs for finite simple groups
AU - Liebeck, Martin W.
AU - Shalev, Aner
AU - Tiep, Pham Huu
N1 - Publisher Copyright:
© 2021, The Hebrew University of Jerusalem.
PY - 2021/3
Y1 - 2021/3
N2 - 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).
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).
UR - http://www.scopus.com/inward/record.url?scp=85102175334&partnerID=8YFLogxK
U2 - 10.1007/s11856-021-2109-1
DO - 10.1007/s11856-021-2109-1
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AN - SCOPUS:85102175334
SN - 0021-2172
VL - 241
SP - 449
EP - 464
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -