[Frostix]

For example: if I where to purchase a group from someone Could I resurrect an old group?

Like the Wrath, RATS crew, etc?

If I recall correctly, since they were official groups you can't reuse their names.

[Aceman]

No you cannot. The only way you would be allowed to do this (from what I've seen) is to have the previous owner as a leader who is fully endorsing your decision. That happened when Complexity (owned by JD) turned into Infamous. iNviZ was a leader and allowed JD to change the group into Infamous v2. Respawn was recreated with Astonish as owner and reused the name as well as graphics I believe. The only exception I can see to a group being founded with the previous owner (of the group's name you wanted to use) is to buy a group and continue with the current path / graphics that are being used. Syrah is selling his group and allowing people to use the name and userbar.

tl-dr;
Have previous owner as leader or buy a group and have the previous owner give you permission to continue using the name.