A -approximate group is a symmetric set containing the identity such that is covered by at most translates of .
If finite sets satisfy , then a maximal family of disjoint translates , with , has at most members and gives
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The concept of an "approximate group" arises in the field of group theory and is particularly relevant in the study of discrete groups, geometric group theory, and number theory. An approximate group can be thought of as a structure that shares some properties with groups but does not necessarily satisfy all group axioms in a strict sense.