In the field of group theory, "strong conjugacy" refers to the property of two elements in a group being conjugate only if they have the same centralizer. Essentially, this means that any two elements which are conjugate to each other are in some way "strongly" related, as they share a specific property within the group. Synonyms for "strong conjugacy" might include concepts like "invariant" or "fixed," as the centralizer of an element in a group is essentially the set of elements that do not change that element when conjugating. Other phrases that could convey similar meanings might include "closely related" or "intimately connected," as the notion of strong conjugacy implies a sort of intrinsic link between the conjugate elements.