Reference: the rotation speed of galaxies in a galaxy cluster:
Is the dark matter associated with each galaxy in a cluster, sufficient to explain the rotation speed of galaxies in the cluster, or extra additional dark matter in the cluster in the intergalactic space is required to explain the galaxy rotation speed in the cluster?
Assuming that by "rotation speed of galaxies in a galaxy cluster" you mean something like orbital speeds (since most galaxies in a cluster have rather radial orbits and don't "rotate" within the cluster):
Yes, you absolutely need extra dark matter in the cluster, outside of the dark matter in the individual galaxies. The mass in a cluster comes primarily in three forms:
If you assume that each individual galaxy has dark matter amounting to about 10 times the baryonic matter (as is the case for most galaxies, including the Milky Way), then the per-galaxy dark matter is only about 10-20% of the total mass. Given that the total dark matter content is about 85% or more, that means $\sim 70$% of the total mass is in the form of dark matter filling the cluster in between the galaxies.
Dark matter is clustered together with galaxies rather than spread across intergalactic space. Larger, more dense galaxies have more dark matter than smaller or more diffuse galaxies. And smaller galaxies that pass through larger galaxies can have their dark matter stripped away. As well, dark matter tends to be out front of moving galaxies, while the normal matter lags behind.
If you look at this map of the bullet cluster of galaxies, you can see the visible and dark matter together and separately. Take care to look at the 4th image where you can clearly see the purple dark matter out in front of the normal matter in pink.
