The strong coupling constant for b quarks has been determined, and its flavour independence, as predicted by QCD, investigated. The analysis involved events with lepton candidates selected from approximately 356 000 hadronic decays of the Z0, collected by the DELPHI detector at LEP in 1990 and 199 1. A method based on a direct comparison of the three-jet fraction in a b enriched sample, selected by requiring leptons with large momenta and transverse momenta, to that of the entire hadronic sample, illustrated the significant effect of the b quark mass on the multi-jet cross section, and verified the flavour independence of the strong coupling constant to an accuracy of +/- 6%. A second procedure based on a fit to the momentum and transverse momentum spectra of the lepton candidates in both two-jet and three (or more)-jet event samples simultaneously determined the b content in each, and, using second order QCD calculations, gave an absolute measurement of alpha(s) for b quarks of 0. 1 18 +/- 0.004 (stat.) +/- 0.003 (syst.) +/- 0.008 (scale). A comparison with a, for all quark flavours, as measured from the three-jet fraction in all hadronic events, further allowed the coupling strength for b quarks to be expressed in terms relative to that for udsc quarks, thereby cancelling certain common systematic uncertainties, and yielded alpha(s)b/alpha(s)udsc = 1.00 +/- 0.04 (stat.) +/- 0.03 (syst.).