An amplitude analysis of an exclusive sample of 5765 events from the reacti
on pi (-) p --> eta ' pi (-) p at 18 GeV/c is described. The eta ' pi (-) p
roduction is dominated by natural parity exchange and by three partial wave
s: those with J(PC) = 1(-+), 2(++), and 4(++). A mass-dependent analysis of
the partial-wave amplitudes indicates the production of the a(2)(1320) mes
on as well as the a(4)(2040) meson, observed for the first time decaying to
eta ' pi (-). The dominant, exotic (non-q (q) over bar) 1(-+) partial wave
is shown to be resonant with a mass of 1.597 +/- 0.010(-0.010)(+0.045) GeV
/c(2) and a width of 0.340 +/- 0.040 +/- 0.050 GeV/c(2). This exotic state,
the pi (1)(1600). is produced with a t dependence which is different from
that of the a(2)(1320) meson, indicating differences between the production
mechanisms for the two states.