Do you think, the Lorentz factor id somehow present in z, or not?
z represents frequency differences which is the same as apparent slowdown (or speedup for blueshift). Note, this is apparent slowdown in the sense of what we see through a telescope, not how much it is "really" slowed down in "our" reference frame.
Now, when we imagine an extending our reference frame to that other galaxy in a particular way such that in that particular extension of our reference frame the slowdown is caused by motion rather than by universe expansion, then we use the relativistic doppler shift formula to get a speed. Th...
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