The Green Regiment was the military unit that Alexander Mackay and Andrew Lennox were part of when Grantville appeared.
By the spring of 1632 (NTL), Mackay led over a thousand men, which led Gustavus Adolphus of Sweden to promote Mackay to colonel. This left Mackay leading a regiment-sized unit within a larger regiment.
Note: it is not clear if the Green Brigade, which fought in the battle that resulted in Gustavus Adolphus being incapacitated, was the same unit, or a successor of it.