I have a basic question about the definition of the Greenberger–Horne–Zeilinger state , which is defined as the maximally entangled state. Why is it only considered applicable for subsystems $M > 2$, why would the definition not apply or why is it not preferable to consider states where $M = 2$?
A GHZ in $M=2$ would be $|00\rangle+|11\rangle$. Sure you could still call it a GHZ, but it is not very useful because this state already has a name: it's a Bell state.
A standard reference to understand entanglement and how it is measured is Gühne and Toth 2008.