The value of the Lr quark, mass at the M-Z scale defined in the <(MS)o
ver bar> renormalization scheme, m(b)(M-Z), was determined using 2.8 m
illion hadronic Z decays collected during 1992-1994 by the DELPHI dete
ctor to be m(b)(M-Z) = 2.67 +/- 0.25 (stat.) +/- 0.34 (frag.) +/- 0.27
(theo.) GeV/c(2). The analysis considers NLO corrections to the three
-jet production rate including mass effects, and the result obtained a
grees with the QCD prediction of having a running b quark mass at an e
nergy scale equal to M-Z. This is the first time that such a measureme
nt is performed far above the <b(b)over bar> production threshold. The
study also verifies the flavour independence of tile strong coupling
constant for b and light quarks within 1% accuracy. (C) 1998 Elsevier
Science B.V.