  The inclusive production of the omega(782) vector meson in hadronic Z decays
is measured and compared to model predictions. The analysis is based on 4
million hadronic Z decays recorded by the ALEPH detector between 1991 and 1995.
The production rate for x_p = p_meson/p_beam > 0.05 is measured in the omega ->
pi^+ pi^- pi^0 decay mode and found to be 0.585 +- 0.019_stat +- 0.033_sys per
event. Inclusive eta meson production is also measured in the same decay
channel for x_p > 0.10, obtaining 0.355 +- 0.011_stat +- 0.024_sys per event.
The branching ratio for omega -> mu^+ mu^- is investigated. A total of 18.1 +-
5.9 events are observed, from which the muonic branching ratio is measured for
the first time to be BR(omega -> mu^+ mu^-) = (9.0 +- 2.9_stat +-
1.1_sys)*10^-5.
