The paper investigates the conditions for full and partial synchronization in systems of coupled chaotic maps that include the presence of a major element, that is, an element that interacts with all the other elements of the system. We consider a system which consists of two globally coupled populations of one-dimensional maps that interact via a major element. The presence of this element can induce synchronization in both of the globally coupled populations even though they operate in different states. If a parameter mismatch is introduced between two populations of uncoupled maps, the presence of a major element is found to provide for the existence of states in which peripheral elements with different parameter values display similar dynamics.